Question:

Evaluate the iterated integral $\displaystyle \int_0^1{\int_\frac{x}{2}^\frac{1}{2}{e^{y^2}}\,dy }\,dx $ by reversing the order of integration.

Is this correct?

current limits are:

$\displaystyle \frac{x}{2} \leq y \leq \frac{1}{2} = x \leq 2y \leq 1$ and $\displaystyle 0 \leq x \leq 1$

rearranging these gives:

$\displaystyle 0 \leq y \leq \frac{1}{2}$ and $\displaystyle 0 \leq x \leq 2y$

making the equation now $\displaystyle \int_0^\frac{1}{2}{\int_0^{2y}{e^{y^2}}\,dx}\,dy $

Correct? yes/no? Want some reassurance before I try to tackle the integration part!