91Ó°ÊÓ

In the following exercises, evaluate the iterated integrals by choosing the order of integration. $$ \int_{1}^{\sqrt{3}} \int_{1}^{2} y \arctan \left(\frac{1}{x}\right) d y d x $$

In the following exercises, evaluate the iterated integrals by choosing the order of integration. $$ \int_{0}^{1} \int_{0}^{1 / 2}(\arcsin x+\arcsin y) d y d x $$

In the following exercises, evaluate the iterated integrals by choosing the order of integration. $$ \int_{0}^{1} \int_{1}^{2} x e^{x+4 y} d y d x $$

In the following exercises, evaluate the iterated integrals by choosing the order of integration. $$ \int_{1}^{2} \int_{0}^{1} x e^{x-y} d y d x $$

In the following exercises, evaluate the iterated integrals by choosing the order of integration. $$ \int_{1}^{e} \int_{1}^{e}\left(\frac{\ln y}{\sqrt{y}}+\frac{\ln x}{\sqrt{x}}\right) d y d x $$

In the following exercises, evaluate the iterated integrals by choosing the order of integration. $$ \int_{1}^{e} \int_{1}^{e}\left(\frac{x \ln y}{\sqrt{y}}+\frac{y \ln x}{\sqrt{x}}\right) d y d x $$

In the following exercises, evaluate the iterated integrals by choosing the order of integration. $$ \int_{0}^{1} \int_{1}^{2}\left(\frac{x}{x^{2}+y^{2}}\right) d y d x $$

In the following exercises, evaluate the iterated integrals by choosing the order of integration. $$ \int_{0}^{1} \int_{1}^{2} \frac{y}{x+y^{2}} d y d x $$

In the following exercises, find the average value of the function over the given rectangles. $$ f(x, y)=-x+2 y, \quad R=[0,1] \times[0,1] $$

In the following exercises, find the average value of the function over the given rectangles. $$ f(x, y)=x^{4}+2 y^{3}, \quad R=[1,2] \times[2,3] $$