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## Homework Statement

Use polar coords to evaluate the double integral x

^{3}+ xy

^{2}dydx from y = -(9-x

^{2})

^{1/2}to (9-x

^{2})

^{1/2}, and x = 0 to 3

## Homework Equations

## The Attempt at a Solution

So the region is a half circle of radius 3, centered @ the origin, with only the possitive x side, (right side of circle)

x = rcosQ, y = rsinQ

the integral is r

^{3}cos

^{3}Q + r

^{3}cosQsinQ drdQ

after integration with respect to r i get and pluging in the limits

84/4 cos^3 Q + 81/4 cosQsinQ dQ

i looked up the integrals of cos^3Q in the back of my book and it is quite complex. Have i made any mistakes thus far, and is there an easier way to evaluate it