ࡱ> *&'()*YZ[\Z {C~v CbjbjVV hx<<<|^y]! &n)wOLOOO6Q6Q6QHJJJJJJ$mJn6Q2Q6Q6Q6QnOOoC6Q=@OOH6QH~ 85XOpupX X4Y0< YlYXYX6Q6Q6Q6Q6Q6Q6Qnn6Q6Q6Q6Q6Q6Q6QY6Q6Q6Q6Q6Q6Q6Q6Q6Q : 15. INTEGRAL (ANTI DIVERENSIAL) A. Integral Tak Tentu 1) Rumus-Rumus Integral Tak Tentu Fungsi Aljabar dan Trigonometri ( dx = x + c ( a dx = a ( dx = ax + c ( xn dx =  EMBED Equation.3 + c ( sin ax dx =  EMBED Equation.3 cos ax + c ( cos ax dx =  EMBED Equation.3 sin ax + c ( sec2 ax dx =  EMBED Equation.3 tan ax + c ( [ f(x) ( g(x) ] dx = ( f(x) dx ( ( g(x) dx Catatan 1. Identitas trigonometri yang biasa digunakan 2sinA(cosB = sin(A + B) + sin(A B) 2sinA(sinB = cos(A + B) cos(A B) sin2A = EMBED Equation.3  cos2A = EMBED Equation.3  sin 2A = 2sin A ( cos A 2. Teknik Penyelesain Bentuk Integran Misalkan u(x) dan v(x) masing-masing adalah fungsi dalam variabel x, maka metode pengintegralan yang bisa digunakan adalah: a. Metode substitusi Jika bentuk integran : ( u v dx , dengan u dan v memiliki hubungan, yaitu v dx = du b. Metode Parsial dengan TANZALIN Jika bentuk integran : ( u dv , dengan u dan v tidak memiliki hubungan, yaitu v dx `" du SOALPENYELESAIANUN 2011 PAKET 12 Hasil  EMBED Equation.3  = & a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  Jawab : c UN 2011 PAKET 46 Hasil  EMBED Equation.3  = a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  Jawab : b UN 2009 PAKET A/B Hasil  EMBED Equation.3  =  EMBED Equation.3  + C  EMBED Equation.3  + C  EMBED Equation.3  + C  EMBED Equation.3  + C  EMBED Equation.3  + C Jawab : c  SOALPENYELESAIANUN 2006 Hasil dari ((x 3)(x2 6x + 1)3 dx =  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Jawab : dUAN 2003 Hasil  EMBED Equation.3 =  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Jawab : bUN 2011 PAKET 12 Hasil dari (cos4 2x sin 2x dx = a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  Jawab : bUN 2011 PAKET 46 Hasil (sin3 3x cos 3x dx = a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  Jawab : e  SOALPENYELESAIANUN 2010 PAKET A Hasil ( (sin2 x cos2 x) dx adalah a.  EMBED Equation.3  cos 2x + C b. 2 cos 2x + C c. 2 sin 2x + C d.  EMBED Equation.3  sin 2x + C e.  EMBED Equation.3  sin 2x + C Jawab : cUN 2010 PAKET B Hasil dari ((3 6 sin2 x) dx = a.  EMBED Equation.3 sin2 2x + C b.  EMBED Equation.3 cos2 2x + C c.  EMBED Equation.3 sin 2x + C d. 3 sin x cos x + C e.  EMBED Equation.3 sin 2x cos 2x + C Jawab : dUN 2009 PAKET A/B Hasil (4sin 5x ( cos 3x dx = 2 cos 8x 2 cos 2x + C  EMBED Equation.3  + C  EMBED Equation.3  + C  EMBED Equation.3  + C  EMBED Equation.3  + C Jawab : bUN 2008 PAKET A/B Hasil dari (sin2 x cos x dx = a.  EMBED Equation.3 cos3 x + C b.  EMBED Equation.3  cos3 x + C c.  EMBED Equation.3  sin3 x + C d.  EMBED Equation.3  sin3 x + C e. 3 sin3 x + C Jawab : d UN 2006 Hasil dari ((x2 3x + 1) sin x dx = (x2 + 3x + 1) cos x + (2x 3) sin x + c (x2 + 3x 1) cos x + (2x 3) sin x + c (x2 3x + 1) sin x + (2x 3) cos x + c (x2 3x + 1) cos x + (2x 3) sin x + c (x2 3x + 3) cos x + (2x 3) sin x + c Jawab : a SOALPENYELESAIANUN 2005 Hasil dari  EMBED Equation.3 = x2 sin x + 2x cos x + c (x2 1) sin x + 2x cos x + c (x2 + 3) sin x 2x cos x + c 2x2 cos x + 2x2 sin x + c 2x sin x (x2 1)cos x + c Jawab : b UN 2004 Hasil dari  EMBED Equation.3 =  EMBED Equation.3 x2 cos 2x  EMBED Equation.3 x sin 2x + EMBED Equation.3 cos 2x + c  EMBED Equation.3 x2 cos 2x + EMBED Equation.3 x sin 2x  EMBED Equation.3 cos 2x + c  EMBED Equation.3 x2 cos 2x + EMBED Equation.3 x sin 2x + EMBED Equation.3 cos 2x + c  EMBED Equation.3 x2 cos 2x  EMBED Equation.3 x sin 2x  EMBED Equation.3 cos 2x + c  EMBED Equation.3 x2 cos 2x  EMBED Equation.3 x sin 2x + EMBED Equation.3 cos 2x + c Jawab : c  2) Penggunaan Integral Tak Tentu Integral tak tentu di gunakan untuk mencari persamaan suatu kurva y = f(x) apabila diketahui turunan pertama dan sebuah titik pada kurva tersebut yaitu: f(x) = (f(x) dx, dengan f(x) adalah turunan pertama dari f(x) atau: y = (  EMBED Equation.3 , dengan  EMBED Equation.3  adalah turunan pertama y SOALPENYELESAIANUN 2004 Gradien garis singgung suatu kurva adalah m =  EMBED Equation.3 = 2x 3. kurva itu melalui titik (3,2). Persamaan kurva tersebut adalah y = x2 3x 2 y = x2 3x + 2 y = x2 + 3x 2 y = x2 + 3x + 2 y = x2 + 3x 1 Jawab : b UAN 2003 Jika grafik y = f(x) melalui titik (1, 2) dan turunannya f(x) = x2 + 1, maka grafiknya y = f(x) memotong sumbu Y di titik (0, 0) (0,  EMBED Equation.3 ) (0,  EMBED Equation.3 ) (0, 1) (0, 2) Jawab : c  KUMPULAN SOAL SKL UN 2011 INDIKATOR 26 (i) Menghitung integral tak tentu fungsi aljabar dan fungsi trigonometri. Hasil dari ((x 3)(x2 6x + 1)3 dx = a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  Hasil dari  EMBED Equation.3 = ... a. EMBED Equation.3(x3 + 3x + 5)  EMBED Equation.3 + C b. EMBED Equation.3(x3 + 3x + 5)  EMBED Equation.3 + C c. EMBED Equation.3(x3 + 3x + 5)2  EMBED Equation.3 + C d. EMBED Equation.3(x3 + 3x + 5)2  EMBED Equation.3 + C e. EMBED Equation.3(x3 + 3x + 5)2 + C Hasil dari  EMBED Equation.3  a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  Hasil  EMBED Equation.3  = a.  EMBED Equation.3  + C b.  EMBED Equation.3  + C c.  EMBED Equation.3  + C d.  EMBED Equation.3  + C e.  EMBED Equation.3  + C Hasil dari  EMBED Equation.3 = ... a.  EMBED Equation.3 + C d. 3 EMBED Equation.3 + C b.  EMBED Equation.2  EMBED Equation.3 + C e. 4 EMBED Equation.3 + C c. 2 EMBED Equation.3 + C Hasil dari  EMBED Equation.3 dx = ... a.  EMBED Equation.2 + C b.  EMBED Equation.2 + C c.  EMBED Equation.2 + C d.  EMBED Equation.2 + C e.  EMBED Equation.2 + C Hasil dari  EMBED Equation.3 dx = ... a.  EMBED Equation.2 + C b.  EMBED Equation.2 + C c.  EMBED Equation.2 + C d.  EMBED Equation.2 + C e.  EMBED Equation.2 + C Hasil  EMBED Equation.3  = a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  Hasil  EMBED Equation.3  = a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  Hasil dari (cos4 2x sin 2x dx = a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  Hasil (sin3 3x cos 3x dx = a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  Hasil dari (sin2 x cos x dx = a.  EMBED Equation.3 cos3 x + C b.  EMBED Equation.3  cos3 x + C c.  EMBED Equation.3  sin3 x + C d.  EMBED Equation.3  sin3 x + C e. 3 sin3 x + C Hasil  EMBED Equation.3 = a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  Hasil (4sin 5x ( cos 3x dx = a. 2 cos 8x 2 cos 2x + C b.  EMBED Equation.3  + C c.  EMBED Equation.3  + C d.  EMBED Equation.3  + C e.  EMBED Equation.3  + C Hasil dari  EMBED Equation.3 = ... . a. (EMBED Equation.3 sin 4x EMBED Equation.3 sin 2x + C b. (EMBED Equation.3 cos 4x EMBED Equation.3 cos 2x + C c. (EMBED Equation.3 cos 4x EMBED Equation.3 cos 2x + C d. EMBED Equation.3 cos 4x EMBED Equation.3 cos 2x + C e. EMBED Equation.3 cos 4x  EMBED Equation.2  cos 2x + C Hasil dari  EMBED Equation.3 dx = ... a. 2 sin 2x + x + C b. sin 2x + x + C c. sin 2x x + C d. (2 sin 2x + x + C e. (cos 2x + x + C Hasil dari  EMBED Equation.3 dx = ... a.  EMBED Equation.3  sin 2x + EMBED Equation.3x + C b.  EMBED Equation.3  sin 2x + EMBED Equation.3x + C c.  EMBED Equation.3  cos 2x + EMBED Equation.3x + C d. ( EMBED Equation.3  sin 2x + EMBED Equation.3x + C e. ( EMBED Equation.3  cos 2x + EMBED Equation.3x + C Hasil dari  EMBED Equation.3 = ... a.  EMBED Equation.3 sin 2x EMBED Equation.3x + C b.  EMBED Equation.3 sin 2x EMBED Equation.3x + C c.  EMBED Equation.3 cos 2x EMBED Equation.3x + C d. ( EMBED Equation.3 cos 2x EMBED Equation.3x + C e. ( EMBED Equation.3 sin 2x EMBED Equation.3x + C Hasil ( (sin2 x cos2 x) dx adalah a.  EMBED Equation.3  cos 2x + C b. 2 cos 2x + C c. 2 sin 2x + C d.  EMBED Equation.3  sin 2x + C e.  EMBED Equation.3  sin 2x + C Hasil dari ((3 6 sin2 x) dx = a.  EMBED Equation.3 sin2 2x + C b.  EMBED Equation.3 cos2 2x + C c.  EMBED Equation.3 sin 2x + C d. 3 sin x cos x + C e.  EMBED Equation.3 sin 2x cos 2x + C Hasil dari ((x2 3x + 1) sin x dx = (x2 + 3x + 1) cos x + (2x 3) sin x + c (x2 + 3x 1) cos x + (2x 3) sin x + c (x2 3x + 1) sin x + (2x 3) cos x + c (x2 3x + 1) cos x + (2x 3) sin x + c (x2 3x + 3) cos x + (2x 3) sin x + c Hasil dari  EMBED Equation.3 = x2 sin x + 2x cos x + c (x2 1) sin x + 2x cos x + c (x2 + 3) sin x 2x cos x + c 2x2 cos x + 2x2 sin x + c 2x sin x (x2 1)cos x + c Hasil dari  EMBED Equation.3 =  EMBED Equation.3 x2 cos 2x  EMBED Equation.3 x sin 2x + EMBED Equation.3 cos 2x + c  EMBED Equation.3 x2 cos 2x + EMBED Equation.3 x sin 2x  EMBED Equation.3 cos 2x + c  EMBED Equation.3 x2 cos 2x + EMBED Equation.3 x sin 2x + EMBED Equation.3 cos 2x + c  EMBED Equation.3 x2 cos 2x  EMBED Equation.3 x sin 2x  EMBED Equation.3 cos 2x + c  EMBED Equation.3 x2 cos 2x  EMBED Equation.3 x sin 2x + EMBED Equation.3 cos 2x + c B. INTEGRAL TENTU Misalkan kurva y = f(x) kontinu pada interval tertutup [a, b], maka luas daerah L yang dibatasi oleh kurva y = f(x), sumbu X, garis x = a, dan garis x = b, ditentukan dengan rumus: L =  EMBED Equation.3 , dengan F(x) adalah integral (antidiferensial) dari f(x) 1) Integral Tentu Fungsi Aljabar dan Trigonometri SOALPENYELESAIANUN 2011 PAKET 12 Hasil  EMBED Equation.3  = a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  Jawab : e UN 2011 PAKET 46 Hasil  EMBED Equation.3  = a. 9 EMBED Equation.3  b. 9 c. 8 d.  EMBED Equation.3  e. 3 Jawab : b UN 2010 PAKET A Hasil dari  EMBED Equation.3  = a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  Jawab : c  SOALPENYELESAIANUN 2010 PAKET B Hasil dari  EMBED Equation.3  = a. 58 b. 56 c. 28 d. 16 e. 14 Jawab : a UN 2009 PAKET A/B Nilai a yang memenuhi persamaan  EMBED Equation.3 = 14 adalah 2 1 0  EMBED Equation.3  1 Jawab : c UN 2008 PAKET A/B Hasil dari  EMBED Equation.3  = a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  Jawab : e UN 2007 PAKET A Diketahui  EMBED Equation.3 = 78. Nilai (2p) = 8 4 0 4 8 Jawab : e  SOALPENYELESAIANUN 2007 PAKET B Diketahui  EMBED Equation.3 = 14. Nilai (4p) = 6 8 16 24 32 Jawab : b EBTANAS 2002 Hasil dari EMBED Equation.3 = 4  EMBED Equation.3  0  EMBED Equation.3   EMBED Equation.3  Jawab : a EBTANAS 2002  EMBED Equation.3 =  EMBED Equation.3 . Nilai a2 = 5 3 1 3 5 Jawab : e UN 2011 PAKET 12 Hasil  EMBED Equation.3  = a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  Jawab : d  SOALPENYELESAIANUN 2011 PAKET 46 Hasil  EMBED Equation.3  = a.  EMBED Equation.3  b.  EMBED Equation.3  c. 1 d. 2 e.  EMBED Equation.3  Jawab : dUN 2010 PAKET A Nilai dari  EMBED Equation.3  = a.  EMBED Equation.3  b.  EMBED Equation.3  c. 0 d.  EMBED Equation.3  e.  EMBED Equation.3  Jawab : aUN 2010 PAKET B Hasil dari  EMBED Equation.3  = a. 1 b.  EMBED Equation.3  c. 0 d.  EMBED Equation.3  e. 1 Jawab : bUN 2004 Nilai dari EMBED Equation.3 =  EMBED Equation.3   EMBED Equation.3  0  EMBED Equation.3   EMBED Equation.3  Jawab : e SOALPENYELESAIANUAN 2003  EMBED Equation.3 = 2 1 0 1 2 Jawab : aUAN 2003  EMBED Equation.3 = a.  EMBED Equation.3  d.  EMBED Equation.3  b.  EMBED Equation.3  e.  EMBED Equation.3  c.  EMBED Equation.3  Jawab : c EBTANAS 2002  EMBED Equation.3 = a.  EMBED Equation.3  d.  EMBED Equation.3  b.  EMBED Equation.3  e.  EMBED Equation.3  c.  EMBED Equation.3  Jawab cEBTANAS 2002  EMBED Equation.3 = a. 0 d.  EMBED Equation.3 ( b.  EMBED Equation.3  e.  EMBED Equation.3 ( c.  EMBED Equation.3  Jawab : bEBTANAS 2002  EMBED Equation.3 = ( + 1 ( 1 1 ( ( + 1 Jawab : b 2) Penggunan Integral Tentu a) Untuk Menghitung Luas Daerah  EMBED PBrush  a. Luas daerah L pada gb. 1 L =  EMBED Equation.3 , untuk f(x) ( 0b. Luas daerah L pada gb. 2 L =  EMBED Equation.3 , atau L =  EMBED Equation.3  untuk f(x) ( 0c. Luas daerah L pada gb. 3 L =  EMBED Equation.3 , dengan f(x) ( g(x) SOALPENYELESAIANUN 2011 PAKET 12 Luas daerah yang dibatasi kurva y = 4 x2 , y = -x + 2 dan 0 d" x d" 2 adalah & a.  EMBED Equation.3 satuan luas b.  EMBED Equation.3 satuan luas c.  EMBED Equation.3 satuan luas d.  EMBED Equation.3  satuan luas e.  EMBED Equation.3  satuan luas Jawab : b UN 2011 PAKET 46 Luas daerah yang dibatasi kurva y = x2 , y = x + 2, sumbu Y dikuadran I adalah a.  EMBED Equation.3 satuan luas b.  EMBED Equation.3 satuan luas c.  EMBED Equation.3 satuan luas d.  EMBED Equation.3  satuan luas e.  EMBED Equation.3  satuan luas Jawab : e  SOALPENYELESAIANUN 2010 PAKET A Luas daerah yang dibatasi parabola y = x2 x 2 dengan garis y = x + 1 pada interval 0 d" x d" 3 adalah & a. 5 satuan luas b. 7 satuan luas c. 9 satuan luas d. 10 EMBED Equation.3  satuan luas e. 10 EMBED Equation.3  satuan luas Jawab : c UN 2010 PAKET B Luas daerah di kuadran I yang dibatasi kurva y = x3, y = x, x = 0, dan garis x = 2 adalah a. 2 EMBED Equation.3  satuan luas b. 2 EMBED Equation.3  satuan luas c. 3 EMBED Equation.3  satuan luas d. 3 EMBED Equation.3  satuan luas e. 4 EMBED Equation.3  satuan luas Jawab : b  SOALPENYELESAIANUN 2009 PAKET A/B Luas daerah yang dibatasi oleh parabola y = x2 6x + 8, garis y = x 2 dan sumbu X dapat dinyatakan dengan  EMBED PBrush   EMBED Equation.3 +  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  +  EMBED Equation.3   EMBED Equation.3  +  EMBED Equation.3  Jawab : e  SOALPENYELESAIANUN 2008 PAKET A/B Luas daerah yang dibatasi oleh kurva y =  EMBED Equation.3 , sumbu X dan 0 d" x d" 8 adalah & a. 6 satuan luas b. 6 EMBED Equation.3  satuan luas c. 17 EMBED Equation.3 satuan luas d. 18 satuan luas e. 18 EMBED Equation.3  satuan luas Jawab : c UN 2007 PAKET A Luas daerah tertutup yang dibatasi oleh kurva x = y2 dan garis y = x  2 adalah & 0 satuan luas 1 satuan luas 4 EMBED Equation.3 satuan luas 6 satuan luas 16 satuan luas Jawab : c UN 2006 Luas daerah tertutup yang dibatasi oleh kurva y = 6x  x2 dan y = x2  2x pada interval 0 d" x d" 5 sama dengan a. 30 satuan luas b. 26 satuan luas c.  EMBED Equation.3 satuan luas d.  EMBED Equation.3  satuan luas e.  EMBED Equation.3  satuan luas Jawab : b UAN 2003 Luas daerah pada kuadran I yang dibatasi oleh kurva y = x2, sumbu Y, dan garis x + y = 12 adalah 57,5 satuan luas 51,5 satuan luas 49,5 satuan luas 25,5 satuan luas 22,5 satuan luas Jawab : e  SOALPENYELESAIANUAN 2003 Luas daerah yang dibatasi oleh kurva y = x2 9x + 15 dan y = x2 + 7x 15 adalah 2 EMBED Equation.3  satuan luas 2 EMBED Equation.3  satuan luas 2 EMBED Equation.3  satuan luas 3 EMBED Equation.3  satuan luas 4 EMBED Equation.3  satuan luas Jawab : a EBTANAS 2002 Luas daerah yang dibatasi parabola y = 8 x2 dan garis y = 2x adalah 36 satuan luas 41 EMBED Equation.3  satuan luas 41 EMBED Equation.3  satuan luas 46 satuan luas 46 EMBED Equation.3  satuan luas Jawab : a  b) Untuk Menghitung Volume Benda Putar  EMBED PBrush  EMBED PBrush V = EMBED Equation.3  atau V = EMBED Equation.3 V = EMBED Equation.3  atau V = EMBED Equation.3  EMBED PBrush  EMBED PBrush V = EMBED Equation.3  atau V = EMBED Equation.3 V = EMBED Equation.3  atau V = EMBED Equation.3  SOALPENYELESAIANUN 2011 PAKET 12 Volum benda putar yang terjadi jika daerah yang dibatasi oleh kurva y = x2, garis y =2x dikuadran I diputar 360( terhadap sumbu X adalah a.  EMBED Equation.3 satuan volum b.  EMBED Equation.3 satuan volum c.  EMBED Equation.3 satuan volum d.  EMBED Equation.3  satuan volum e.  EMBED Equation.3  satuan volum Jawab : d UN 2010 PAKET A Volum benda putar yang terjadi jika daerah yang dibatasi oleh kurva y = 2x x2 dan y = 2 x diputar mengelilingi sumbu X sejauh 360( adalah a.  EMBED Equation.3 ( satuan volum b.  EMBED Equation.3 ( satuan volum c.  EMBED Equation.3 ( satuan volum d.  EMBED Equation.3 ( satuan volum e. ( satuan volum Jawab : a  SOALPENYELESAIANUN 2010 PAKET B Volum benda putar yang terjadi bila daerah yang dibatasi oleh kurva y = x2 dan y =  EMBED Equation.3  diputar mengelilingi sumbu X sejauh 360( adalah a.  EMBED Equation.3 ( satuan volum b.  EMBED Equation.3 ( satuan volum c.  EMBED Equation.3 ( satuan volum d.  EMBED Equation.3 ( satuan volum e. 2( satuan volum Jawab : a UN 2009 PAKET A/B Perhatikan gambar di bawah ini: Jika daerah yang diarsir pada gambar diputar mengelilingi sumbu X sejauh 360( maka volume benda putar yang terjadi adalah satuan volume  EMBED PBrush   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Jawab : c  SOALPENYELESAIANUN 2008 PAKET A/B Daerah yang dibatasi oleh kurva y = 4 x, x = 1, x = 3, dan sumbu X diputar mengelilingi sumbu X sejauh 360(, maka volume benda putar yang terjadi adalah a. 4 EMBED Equation.3 ( satuan volume b. 6 EMBED Equation.3 ( satuan volume c. 8 EMBED Equation.3 ( satuan volume d. 10 EMBED Equation.3 ( satuan volume e. 12 EMBED Equation.3 ( satuan volume Jawab : c UN 2007 PAKET A Volum benda putar yang terjadi jika daerah yang dibatasi oleh kurva y = 2x dan parabola y = x2 diputar sejauh 360 mengelilingi sumbu X adalah  EMBED Equation.3 ( satuan volume  EMBED Equation.3 ( satuan volume  EMBED Equation.3 ( satuan volume  EMBED Equation.3 ( satuan volume  EMBED Equation.3 ( satuan volume Jawab : b UN 2007 PAKET A Volum benda putar yang terjadi jika daerah yang dibatasi oleh kurva y = x2 + 1 dan y = 3 diputar mengelilingi sumbu Y sejauh 360 adalah 2( satuan volum. 2 EMBED Equation.3 22( satuan volum. 3( satuan volum. 4 EMBED Equation.3 ( satuan volum. 5( satuan volum. Jawab : a  SOALPENYELESAIANUN 2005 Volum benda putar yang terjadi karena daerah yang dibatasi oleh parabola y = x2 dan y2 = 8x diputar 360 mengelilingi sumbu Y adalah . 2 EMBED Equation.3 ( satuan volum 3 EMBED Equation.3 ( satuan volum 4 EMBED Equation.3 ( satuan volum 5 EMBED Equation.3 ( satuan volum 9 EMBED Equation.3 ( satuan volum Jawab : c UAN 2003 Volum benda putar yang terjadi karena daerah yang dibatasi oleh sumbu X, sumbu Y, dan kurva y =  EMBED Equation.3 diputar terhadap sumbu Y sejauh 360, dapat dinyatakan dengan  EMBED Equation.3 dy satuan volume  EMBED Equation.3 dy satuan volume  EMBED Equation.3 dy satuan volume  EMBED Equation.3 dy satuan volume  EMBED Equation.3 dy satuan volume Jawab : a  SOALPENYELESAIANEBTANAS 2002 Gambar berikut merupakan kurva dengan persamaan y = x EMBED Equation.3 . Jika daerah yang diarsir diputar mengelilingi sumbu X, maka volum benda putar yang terjadi sama dengan  EMBED PBrush  6( satuan volum 8( satuan volum 9( satuan volum 10( satuan volum 12( satuan volum Jawab : b KUMPULAN SOAL INDIKATOR 26 (ii) UN 2011 Menghitung integral tentu fungsi aljabar dan fungsi trigonometri. Hasil  EMBED Equation.3  = a.  EMBED Equation.3  c.  EMBED Equation.3  e.  EMBED Equation.3  b.  EMBED Equation.3  d.  EMBED Equation.3  Hasil  EMBED Equation.3  = a. 9 EMBED Equation.3  c. 8 e. 3 b. 9 d.  EMBED Equation.3  Hasil dari  EMBED Equation.3  = a.  EMBED Equation.3  c.  EMBED Equation.3  e.  EMBED Equation.3  b.  EMBED Equation.3  d.  EMBED Equation.3  Hasil dari  EMBED Equation.3  = a. 58 c. 28 e. 14 b. 56 d. 16 Hasil dari EMBED Equation.3 = a. 4 c. 0 e.  EMBED Equation.3  b.  EMBED Equation.3  d.  EMBED Equation.3  Nilai a yang memenuhi persamaan  EMBED Equation.3 = 14 adalah a. 2 c. 0 e. 1 b. 1 d.  EMBED Equation.3  Hasil dari  EMBED Equation.3  = a.  EMBED Equation.3  c.  EMBED Equation.3  e.  EMBED Equation.3  b.  EMBED Equation.3  d.  EMBED Equation.3  Hasil  EMBED Equation.3  = a.  EMBED Equation.3  c.  EMBED Equation.3  e.  EMBED Equation.3  b.  EMBED Equation.3  d.  EMBED Equation.3  Hasil  EMBED Equation.3  = a.  EMBED Equation.3  c. 1 e.  EMBED Equation.3  b.  EMBED Equation.3  d. 2 Nilai dari  EMBED Equation.3  = a.  EMBED Equation.3  c. 0 e.  EMBED Equation.3  b.  EMBED Equation.3  d.  EMBED Equation.3  Hasil dari  EMBED Equation.3  = a. 1 c. 0 e. 1 b.  EMBED Equation.3  d.  EMBED Equation.3   EMBED Equation.3 = a. 2 c. 0 e. 2 b. 1 d. 1  EMBED Equation.3 = a. ( + 1 c. 1 e. ( + 1 b. ( 1 d. (  EMBED Equation.3 = a.  EMBED Equation.3  c.  EMBED Equation.3  e.  EMBED Equation.3  b.  EMBED Equation.3  d.  EMBED Equation.3   EMBED Equation.3 = a.  EMBED Equation.3  c.  EMBED Equation.3  e.  EMBED Equation.3  b.  EMBED Equation.3  d.  EMBED Equation.3  Nilai dari EMBED Equation.3 = a.  EMBED Equation.3  c. 0 e.  EMBED Equation.3  b.  EMBED Equation.3  d.  EMBED Equation.3   EMBED Equation.3 = a. 0 c.  EMBED Equation.3  e.  EMBED Equation.3 ( b.  EMBED Equation.3  d.  EMBED Equation.3 ( Hasil dari  EMBED Equation.3  a. -1 c. 1 e. (3 b. 0 d. (2 Diberikan  EMBED Equation.3 . Nilai a = ... a. 1 c. 3 e. 6 b. 2 d. 4 Di berikan  EMBED Equation.3 . Nilai a2 + a = ... . a. 2 c. 6 e. 24 b. 3 d. 12 Diketahui  EMBED Equation.3 = 78. Nilai  EMBED Equation.3 = ... a. 4 c. 8 e. 12 b. 6 d. 9 Diketahui  EMBED Equation.3 = 78. Nilai (2p) = a. 8 c. 0 e. 8 b. 4 d. 4 Diketahui  EMBED Equation.3 = 14. Nilai (4p) = a. 6 c. 16 e. 32 b. 8 d. 24  EMBED Equation.3 =  EMBED Equation.3 . Nilai a2 = a. 5 c. 1 e. 5 b. 3 d. 3 KUMPULAN SOAL INDIKATOR 27 UN 2011 Menghitung luas daerah dan volume benda putar dengan menggunakan integral. Luas daerah yang dibatasi parabola y = x2  x  2 dengan garis y = x + 1 pada interval 0 d" x d" 3 adalah & satuan luas a. 5 c. 9 e. 10 EMBED Equation.3  b. 7 d. 10 EMBED Equation.3  Luas daerah yang dibatasi kurva y = 4  x2 , y = -x + 2 dan 0 d" x d" 2 adalah & satuan luas a.  EMBED Equation.3  c.  EMBED Equation.3  e.  EMBED Equation.3  b.  EMBED Equation.3  d.  EMBED Equation.3  Luas daerah yang dibatasi kurva y = x2 , y = x + 2, sumbu Y dikuadran I adalah a.  EMBED Equation.3  c.  EMBED Equation.3  e.  EMBED Equation.3  b.  EMBED Equation.3  d.  EMBED Equation.3  Luas daerah di kuadran I yang dibatasi kurva y = x3, y = x, x = 0, dan garis x = 2 adalah satuan luas a. 2 EMBED Equation.3  c. 3 EMBED Equation.3  e. 4 EMBED Equation.3  b. 2 EMBED Equation.3  d. 3 EMBED Equation.3  Luas daerah yang dibatasi oleh kurva y =  EMBED Equation.3 , sumbu X dan 0 d" x d" 8 adalah & satuan luas a. 6 c. 17 EMBED Equation.3  e. 18 EMBED Equation.3  b. 6 EMBED Equation.3  d. 18 Luas yang dibatasi oleh kurva y = 2x2  8, dan sumbu X, pada 0 d" x d" 3 adalah .... satuan luas a. 10 EMBED Equation.3  c. 15 EMBED Equation.3  e. 17 EMBED Equation.3  b. 13 EMBED Equation.3  d. 16 EMBED Equation.3  Luas daerah tertutup yang dibatasi oleh kurva x = y2 dan garis y = x 2 adalah satuan luas a. 0 c. 4 EMBED Equation.3  e. 16 b. 1 d. 6 Luas daerah tertutup yang dibatasi oleh kurva y = 6x x2 dan y = x2  2x pada interval 0 d" x d" 5 sama dengan & satuan luas a. 30 c.  EMBED Equation.3  e.  EMBED Equation.3  b. 26 d.  EMBED Equation.3  Luas daerah yang dibatasi oleh kurva y = x2  9x + 15 dan y =  x2 + 7x  15 adalah & satuan luas a. 2 EMBED Equation.3  c. 2 EMBED Equation.3  e. 4 EMBED Equation.3  b. 2 EMBED Equation.3  d. 3 EMBED Equation.3  Luas daerah pada kuadran I yang dibatasi oleh kurva y = x2, sumbu Y, dan garis x + y = 12 adalah satuan luas a. 57,5 c. 49,5 e. 22,5 b. 51,5 d. 25,5 Luas daerah yang dibatasi parabola y = 8 x2 dan garis y = 2x adalah satuan luas a. 36 c. 41 EMBED Equation.3  e. 46 EMBED Equation.3  b. 41 EMBED Equation.3  d. 46 Luas daerah yang dibatasi oleh kurva y = 9 x2 dan garis y = x + 3 adalah.... satuan luas a. 2  EMBED Equation.3  c. 19  EMBED Equation.3  e. 21  EMBED Equation.3  b. 3  EMBED Equation.3  d. 20  EMBED Equation.3  Volum benda putar yang terjadi jika daerah yang dibatasi oleh kurva y = 2x x2 dan y = 2 x diputar mengelilingi sumbu X sejauh 360( adalah satuan volum a.  EMBED Equation.3 ( c.  EMBED Equation.3 ( e. ( b.  EMBED Equation.3 ( d.  EMBED Equation.3 ( Volum benda putar yang terjadi bila daerah yang dibatasi oleh kurva y = x2 dan y =  EMBED Equation.3  diputar mengelilingi sumbu X sejauh 360( adalah satuan volum a.  EMBED Equation.3 ( c.  EMBED Equation.3 ( e. 2( b.  EMBED Equation.3 ( d.  EMBED Equation.3 ( Daerah yang dibatasi oleh kurva y = 4 x, x = 1, x = 3, dan sumbu X diputar mengelilingi sumbu X sejauh 360(, maka volume benda putar yang terjadi adalah satuan volum a. 4 EMBED Equation.3 ( c. 8 EMBED Equation.3 ( e. 12 EMBED Equation.3 ( b. 6 EMBED Equation.3 ( d. 10 EMBED Equation.3 ( Volum benda putar yang terjadi jika daerah yang dibatasi oleh kurva y = 2x dan parabola y = x2 diputar sejauh 360 mengelilingi sumbu X adalah satuan volum a.  EMBED Equation.3 ( c.  EMBED Equation.3 ( e.  EMBED Equation.3 ( b.  EMBED Equation.3 ( d.  EMBED Equation.3 ( Volum benda yang terjadi, jika daerah yang dibatasi oleh kurva  EMBED Equation.3  dan garis  EMBED Equation.3  diputar mengelilingi sumbu X sejauh 360o adalah satuan volum a.  EMBED Equation.3 ( c.  EMBED Equation.3  ( e.  EMBED Equation.3 ( b.  EMBED Equation.3  ( d.  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EMBED Equation.3 ( c. 5 ( e.  EMBED Equation.3 ( b. 2 ( d. 9 ( Gambar berikut merupakan kurva dengan persamaan y = x EMBED Equation.3 . Jika daerah yang diarsir diputar mengelilingi sumbu X, maka volum benda putar yang terjadi sama dengan satuan volum  EMBED PBrush  a. 6( c. 9( e. 12( b. 8( d. 10( Volum benda putar yang terjadi karena daerah yang dibatasi oleh sumbu X, sumbu Y, dan kurva y =  EMBED Equation.3 diputar terhadap sumbu Y sejauh 360, dapat dinyatakan dengan  EMBED Equation.3 dy satuan volum  EMBED Equation.3 dy satuan volum  EMBED Equation.3 dy satuan volum  EMBED Equation.3 dy satuan volum  EMBED Equation.3 dy satuan volum Perhatikan gambar di bawah ini: Jika daerah yang diarsir pada gambar diputar mengelilingi sumbu X sejauh 360( maka volume benda putar yang terjadi adalah satuan volum  EMBED PBrush  a.  EMBED Equation.3  c.  EMBED Equation.3  e.  EMBED Equation.3  b.  EMBED Equation.3  d.  EMBED Equation.3  Volume benda putar yang terjadi jika daerah yang dibatasi oleh sumbu Y, kurva y = EMBED Equation.3, garis y = 2, dan y =5 diputar mengelilingi sumbu Y dalah satuan volum a. 3 c. 9 e. 11 b. 4 d. 10 Perhatikan gambar berikut!  Jika daerah yang diarsir diputar mengelilingi sumbu-X sejauh 360(, maka volume benda putar yang terjadi adalah ... satuan volum a. EMBED Equation.3( c.  EMBED Equation.3 ( e.  EMBED Equation.3 ( b. EMBED Equation.3( d.  EMBED Equation.3 ( Perhatikan gambar berikut!  Jika daerah yang diarsir diputar mengelilingi sumbu-X sejauh 360(, maka volume benda putar yang terjadi adalah ... satuan volum a. 16( c.  EMBED Equation.3 ( e.  EMBED Equation.3 ( b. EMBED Equation.3( d.  EMBED Equation.3 ( Perhatikan gambar berikut!  Jika daerah yang diarsir diputar mengelilingi sumbu-Y sejauh 360(, maka volume benda putar yang terjadi adalah ... a.  EMBED Equation.2 ( c.  EMBED Equation.3 ( e.  EMBED Equation.3 ( b.  EMBED Equation.3 ( d.  EMBED Equation.3 (     PAGE  LATIH UN Prog. IPA Edisi 2011 http://www.soalmatematik.com PAGE  PAGE 156 INFORMASI PENDIDIKAN http://ibnufajar75.blogspot.com LATIH UN Prog. 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