L24 Math 233 Lecture Notes - Lecture 29: Iterated Integral, Polar Coordinate System, Nissan L Engine
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( 1 2 + y2 = 1. L24 math 233 lecture 29- applications of polar coordinates. Find the volume of the solid bounded by the xy plane, the surface inside the cylinder x. Idea: treat the solid as the region under the graph. This domain could be type i or type ii. After setting up the iterated integral, you have bounds with square roots. To avoid the square roots, use a polar description r 2 cos ( 1 2 + y2 = ( x. 1 2 + r2 sin r2 2 rcos . , any is a solution at the origin. If we treat r as though it"s greater than 0, we can divide by r to get. To find the volume use an iterated integral. Note: this will require integration by parts in the final steps. From there, you can graph the polar curve. Other polar graphs: r = 2 sin r = 2 cos .
