Example 5-6-5 - Maple Help



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 , , .

 a) Integrate $f\left(x,y\right)=\left({x}^{2}+{y}^{2}\right)/{y}^{2}$ over $R$, noting that it takes two iterations to cover $R$. Hint: Solve each bounding curve for $x=x\left(y\right)$ and integrate in the order .
 b) Make the change of variables $u={x}^{2}+{y}^{2}$, $v=x/y$ and evaluate the integral of $f$ over the image of $R$ under this change of variables.