# Math Help - Double Integrals

1. ## Double Integrals

Evaluate the integral by reversing the order of integration.

The integrand is e^x^2 with x limits of 8y to 8 and y limits of 0 to 1

2. Hello,
Originally Posted by Snooks02
Evaluate the integral by reversing the order of integration.

The integrand is e^x^2 with x limits of 8y to 8 and y limits of 0 to 1
$\int_0^1 \int_{8y}^8 e^{x^2} ~ dx ~ dy$

$8y \leq x \leq 8$
$0 \leq y \leq 1$

$8y \leq x \implies y \leq \tfrac x8$ and $0 \leq y$. Hence $\boxed{0 \leq y \leq \tfrac x8}$

Similarly, we get $\boxed{0 \leq x \leq 8}$

So the new integral is :

$\int_0^8 \int_0^{x/8} e^{x^2} ~dy ~dx=\int_0^8 e^{x^2} \left(\int_0^{x/8} dy \right) ~dx$