# Calculate: {eq}\int_{-3}^{3} \int_{0}^{\frac{\pi}{2}} \, (y + y^2 \cos x) \, \mathrm{d}x \, \mathrm{d}y {/eq}.

## Question:

Calculate: {eq}\int_{-3}^{3} \int_{0}^{\frac{\pi}{2}} \, (y + y^2 \cos x) \, \mathrm{d}x \, \mathrm{d}y {/eq}.

## Iterated Integrals:

We generally evaluate double integrals as iterated integrals. To integrate {eq}\int_a^b \int_c^d f(x,y)\, dy\, dx {/eq}, we first integrate {eq}f {/eq} assuming that {eq}x {/eq} is a constant and then evaluate the result with {eq}c {/eq} and {eq}d {/eq} for {eq}y {/eq}. Finally we integrate the result with respect to {eq}x {/eq}.

If the roles of the variables are reversed we integrate with respect to {eq}x {/eq} first and then {eq}y {/eq}.