Example 5-6-5 - Maple Help

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Chapter 5: Double Integration

Section 5.6: Changing Variables in a Double Integral

Example 5.6.5

Let R be the region bounded by the curves C1:16x2y+16y3+8x88 y=0, C2:144x2y+144y324 x120 y=0, C3:16x2y+16y38 x8 y=0.

a) 

Integrate fx,y=x2+y2/y2 over R, noting that it takes two iterations to cover R. Hint: Solve each bounding curve for x=xy and integrate in the order dx dy.

b) 

Make the change of variables u=x2+y2, v=x/y and evaluate the integral of f over the image of R under this change of variables.