My book gives the integral $$\int_0^2 \int_x^2 x\sqrt{1+y^3} dydx$$
And the directions say to sketch the region of integration, and evaluate the integral by switching the order of integration.
Once I have the region sketched out I think I know how to find the area by changing it to $dxdy$, but I'm lost at how to draw the region. Up to now, when we had iterated integrals representing regions, they were always of the form $$\int_b^a \int_{g(x)}^{f(x)} dydx$$or $$\int_b^a \int_{g(y)}^{f(y)} dxdy$$
I know how to draw the region for these where the integrand is $1$, but I've never encountered one where the integrand isn't $1$.