# Thread: evaluate this impossible integral

1. ## evaluate this impossible integral

evaluate this impossible integral
$\int_0^1\int_{3y}^3 e^{x^2}dxdy$
i think there's some way to rearrange this to make it possible, but i don't know how

2. Originally Posted by Rubberduckzilla
evaluate this impossible integral
$\int_0^1\int_{3y}^3 e^{x^2}dxdy$
i think there's some way to rearrange this to make it possible, but i don't know how
Reverse the order of integration.

Looking at the limits on the integration we have

$0 \leq y \leq 1$ and $3y \leq x \leq 3$.

Some rearrangement gives

$0 \leq y \leq \frac{1}{3}x$ and $0 \leq x \leq 3$.

So the integral becomes

$\int_0^3{\int_0^{\frac{1}{3}x}{e^{x^2}\,dy}\,dx}$