Sec 1 2 sqrt

• [PDF File]Math 133 Reverse Trig Substitution R - Michigan State University

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  x2 1. We convert such forms into trigonometric integrals, which at rst seems to complicate them. However, we take careful advantage of the Pythagorean identities cos2( )+sin2( ) = 1 and tan2( )+ 1 = sec2( ), so that the resulting trig formulas simplify to do-able integrals. Our rst example is Rp 1 x2 dx, which computes area under a unit semi ...

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• [PDF File]Trig Substitution - Florida State University

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  1 p x2 9 dx = Z 1 3tan (3sec tan d ) = Z sec d : This can be integrated directly using a clever trick, but should probably instead be considered an integral you should know. Example 2. Compute Z 1 (x2 9)2 dx Soluion: This is almost identical to the rst example. Again, no u-substitution will work, and even though we have no square roots, we can ...

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• [PDF File]Inv trig fns

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  u = inv sec (x) = 1.347 radians 1 x b = Sqrt( x^ 2 - 1 ) tan (u) = opp / adj u u = inv sec (x) tan ( inv sec (x) ) = Sqrt( x^2 - 1 ) sec (u) = x = x/1 = hyp / adj Make hyp = x and adj = 1 . Drawing the angle u = inv sec (x) when x > 1 : y = sec-1 x 3pi/2 y* x* y 3 2-10 -5 -3 3 5 10 1 pi/6 pi/3 pi/2 2pi/3 5pi/6 pi-pi/6-1 1 x

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• [PDF File]TRIGONOMETRY LAWS AND IDENTITIES - CSUSM

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  TRIGONOMETRY LAWS AND IDENTITIES DEFINITIONS Opposite Hypotenuse sin(x)= csc(x)= Hypotenuse 2Opposite 2 Adjacent Hypotenuse cos(x)= sec(x)= Hypotenuse Adjacent

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• [PDF File]Trigonometric Substitution - Stewart Calculus

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  x a sec ,0 sec2 1 tan2 2 or22s 3 2 x a x2 a tan , 1 tan2 sec2 2 2 sa x2 x a sin , 1 sin222 cos2 2 2 sa x. Since this is an indefinite integral, we must return to the ...

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• [PDF File]Trigonometric Substitution - University of South Carolina

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  9x2 −1 dx 16. ˆ x √ x2 −7 dx 17. ˆ√ 1+x2 x dx 18. ˆ 1 √ 25−x2 dx Challenge Problems Below are some harder problems that require a little more thinking/algebraic manipulation to make the substitutions work. 1. ˆp 5+4x−x2 dx 2. ˆ 1 √ x2 −6x+13 dx 3. ˆ x √ x2 + x+1 dx 4. ˆ x2 (3+4x −4x2)3/2 dx 5. ˆp x2 +2xdx 6. ˆ x2 ...

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• [PDF File]Chapter 7: Trigonometric Equations and Identities

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  t sec( ) 2 0 Isolate the secant t sec( ) 2 Rewrite as a cosine 2 cos( ) 1 t Invert both sides 2 1 tcos( ) This gives two solutions 3 t or 3 5 t These are the only two solutions on the interval. By utilizing technology to graph ft t t() 3sec() 5sec() 2 2, a look at a graph

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