# Triple integration

• Jun 5th 2009, 08:41 PM
juicysharpie
Triple integration
http://www.webassign.net/www32/latex...3636a4faff.gif

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?
• Jun 5th 2009, 08:48 PM
matheagle
5xe^-y^2/-2y, is wrong.

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

Let $\displaystyle u=-y^2$.
• Jun 5th 2009, 08:48 PM
Spec
Quote:

Originally Posted by juicysharpie
http://www.webassign.net/www32/latex...3636a4faff.gif

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).

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