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Set up integrals for both orders of integration. Use the more convenient order to evaluate the integral over the region $R$. $\int_{R} \int\left(x^{2}+y^{2}\right) ...

Question

Set up integrals for both orders of integration. Use the more convenient order to evaluate the integral over the region $R$. $\int_{R} \int\left(x^{2}+y^{2}\right) d A$ $R:$ semicircle bounded by $y=\sqrt{4-x^{2}}, y=0$

Set up integrals for both orders of integration. Use the more convenient order to evaluate the integral over the region $R$. $\int_{R} \int\left(x^{2}+y^{2}\right) d A$ $R:$ semicircle bounded by $y=\sqrt{4-x^{2}}, y=0$



Answers

Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order and explain why it's easier.

$ \displaystyle \iint\limits_D y^2 e^{xy}\ dA $, $ D $ is bounded by $ y = x $, $ y = 4 $, $ x = 0 $


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