Can someone check to see if my integration is correct experienced integrators.
Cant use this latex view attachment
You can't possibly have even set up the double integral properly - if you are integrating with respect to $\displaystyle \displaystyle y$ first then your innermost bounds need a function of $\displaystyle \displaystyle x$, not $\displaystyle \displaystyle y$.
Please post the entire question.
ummm no Prove it is correct. You have written
$\displaystyle \int_{0}^{4}\int_{\sqrt{y}}^{2}\frac{ye^{x^2}}{x^3 }dydx$
Do you See the problem with what you posted. You are integrating with respect to y first and have it as a function of y. That does not make sense. After integration you would still have y's in your integrand but no y differential.