ࡱ> DFC xmbjbj 4t&&iiuB.1;1111B3B3B3B3B3B3BCF3B91.1113Bii;lB4441Xip;1B411B446<W^y=; n̜1<BB0B=dG1`G8y=y=G=114111113B3BH3`111B1111G111111111& /:  Ch 8.3 Wkst AP Calculus BC Name: Area, Arc Length, and Slope of Polar Coordinates  Objective: to use integrals to calculate area, arc length, and slope of Polar Coordinates.  For a polar curve,  EMBED Equation.3 , with  EMBED Equation.3 , the Area from  EMBED Equation.3  to  EMBED Equation.3  is  EMBED Equation.3 . For a polar curve,  EMBED Equation.3 , the Arc Length of the Polar Curve = Distance Traveled from  EMBED Equation.3  to  EMBED Equation.3  ,   EMBED Equation.3 , where . This can be shown to be equivalent to  EMBED Equation.3  . . For a polar curve,  EMBED Equation.3 , the Slope of the Polar Curve at  EMBED Equation.3  is  EMBED Equation.3  , where .  Example 1: Find the area inside the cardioid  EMBED Equation.3  for  EMBED Equation.3 . NO CALCULATOR.  Example 2: Find the length of the polar equation  EMBED Equation.3  for  EMBED Equation.3 . CALCULATOR REQUIRED. Example 3: Find the slope of the curve  EMBED Equation.3  at  EMBED Equation.3 . NO CALCULATOR. Ch 8.3 Wkst AP Calculus BC Name: Area, Arc Length, and Slope of Polar Coordinates  For a polar curve,  EMBED Equation.3 , with  EMBED Equation.3 , the Area from  EMBED Equation.3  to  EMBED Equation.3  is  EMBED Equation.3 . For a polar curve,  EMBED Equation.3 , the Arc Length of the Polar Curve = Distance Traveled from  EMBED Equation.3  to  EMBED Equation.3  ,   EMBED Equation.3 , where . This can be shown to be equivalent to  EMBED Equation.3  . . For a polar curve,  EMBED Equation.3 , the Slope of the Polar Curve at  EMBED Equation.3  is  EMBED Equation.3  , where .  1. Find the area bounded by the spiral  EMBED Equation.3  and  EMBED Equation.3 . NO CALCULATOR.  2. Find the area of one petal of the rose  EMBED Equation.3 . NO CALCULATOR.  3. Find the area of the region that is bounded by the graphs of the  EMBED Equation.3 ,  EMBED Equation.3 , and  EMBED Equation.3 . CALCULATOR REQUIRED.  4. Find the area inside the cardioid  EMBED Equation.3  and outside the circle  EMBED Equation.3 . CALCULATOR REQUIRED.  5. Find the length of the spiral  EMBED Equation.3  for  EMBED Equation.3 . CALCULATOR REQUIRED.  6. Find the length of one petal of the rose  EMBED Equation.3  for  EMBED Equation.3 . CALCULATOR REQUIRED.  7. If  EMBED Equation.3 , then at what values of  EMBED Equation.3  is  EMBED Equation.3  on [ 0 , 2 ]? CALCULATOR REQUIRED.  8. For what values of  EMBED Equation.3  on the polar curve  EMBED Equation.3 , for  EMBED Equation.3 , are the tangent lines horizontal? vertical? CALCULATOR REQUIRED.  9. Find the maximum value of the y-coordinate of points on the polar curve  EMBED Equation.3 . SCIENTIFIC CALCULATOR REQUIRED, BUT NO GRAPHING CALCULATOR.   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