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Using polar coordinates to evaluate iterated integrals: Sketch the region determined by the limits of the given iterated integrals, and then evaluate the integrals.

0π/202sinθr3drdθ

Short Answer

Expert verified

0π/202sinθr3drdθ=34π

Step by step solution

01

Draw the region

The region determined by the limits is shown below,

02

Evaluate the integral

I=0π/202sinθr3drdθI=0π/2r4402sinθdθI=1640π/2sin4θdθI=40π/2sin4θdθI=434·12·π2I=34π

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