# Math Help - Triple integration

1. ## Triple integration

I integrated w/ respect to x and got 5xze^-y^2. Plugging in the limits of integration, I got 5yze^-y^2. Then integrating with respect to y, I got 5xe^-y^2/-2y. Plugging in the limits of integration, I then get: 5xe^-z^2/-2z. Am I on the right track?

2. 5xe^-y^2/-2y, is wrong.

$\int ye^{-y^2}dy$ needs to be solved via substitution.

Let $u=-y^2$.

3. Originally Posted by juicysharpie

I integrated w/ respect to x and got 5xze^-y^2. Plugging in the limits of integration, I got 5yze^-y^2. Then integrating with respect to y, I got 5xe^-y^2/-2y. Plugging in the limits of integration, I then get: 5xe^-z^2/-2z. Am I on the right track?
Almost (note the blue part that I added).

$\int 5z\cdot ye^{-y^2}dy=5z\cdot -\frac{e^{-y^2}}{2}$