Activity 12.3.3

Let $f(x,y) = x+y^2$ on the rectangle $R$ with $0\leq x\leq 2$ and $0\leq y\leq 3$.

1. Evaluate $\displaystyle{\iint_R f(x,y) \, dA}$ using an iterated integral. Choose an order for integration by deciding whether you want to integrate first with respect to $x$ or $y$.

2. Evaluate $\displaystyle{\iint_R f(x,y) \, dA}$ using the iterated integral whose order of integration is the opposite of the order you chose in (a).