# Double intergral

• Apr 24th 2009, 03:00 PM
DMDil
Double intergral
Find https://webwork.uncc.edu/webwork2_fi...7ce48c36e1.png

I usually know how to do double integrals, but i have no idea how to deal with this one. plz help me solve/understand this.
• Apr 24th 2009, 03:02 PM
mr fantastic
Quote:

Originally Posted by DMDil
Find https://webwork.uncc.edu/webwork2_fi...7ce48c36e1.png

I usually know how to do double integrals, but i have no idea how to deal with this one. plz help me solve/understand this.

The integrand is seperable in the variables: $\displaystyle x e^x y e^y$. So it becomes the product of two seperate integrals, each of which can be done using integration by parts.
• Apr 24th 2009, 03:03 PM
Jhevon
Quote:

Originally Posted by DMDil
Find https://webwork.uncc.edu/webwork2_fi...7ce48c36e1.png

I usually know how to do double integrals, but i have no idea how to deal with this one. plz help me solve/understand this.

integrate with respect to y first and then with respect to x, plugging in the limits as you go. note, when integrating with respect to y, treat x as a constant, and vice versa.

you need integration by parts here. to start off, let $\displaystyle u = xy$ and $\displaystyle dv = e^{x + y}~dy$ (remember, x is a constant!)

Quote:

Originally Posted by mr fantastic
The integrand is seperable in the variables: $\displaystyle x e^x y e^y$. So it becomes the product of two seperate integrals, each of which can be done using integration by parts.

hehe, even nicer :D
• Apr 24th 2009, 03:05 PM
Jester
Quote:

Originally Posted by DMDil
Find https://webwork.uncc.edu/webwork2_fi...7ce48c36e1.png

I usually know how to do double integrals, but i have no idea how to deal with this one. plz help me solve/understand this.

Since you're on a rectangle and the expontential spilts up then

$\displaystyle \int_4^7 x e^x dx \int_5^7 y e^y dy$ then parts on each part.