Question

Evaluate the triple integral ye^(-xy) dV where B is the box determined by x between 0 and 2, y between 0 and 4, and z between 0 and 4.

Answer 1

Where are you stuck?

Answer 2

Just how to integrate the function.

Answer 3

It's been awhile since I've done integrals.

Answer 4

Well try to set it up and when you're wrong I'll fix it and explain it.

Answer 5

I have that part done. One sec . . ..

Answer 6

\[\int\limits_{0}^{4}\int\limits_{0}^{2}\int\limits_{0}^{4} ye ^{-xy} dz dx dy\]

Answer 7

Ok good so far, Now just start from the inside out. You've put z first, which is a good choice since there aren't any z's here. That means with respect to z, all of that is a constant, which means your first step will look pretty simple: \[\int\limits_{0}^{4}\int\limits_{0}^{2} ye ^{-xy}z |_0^4dx dy\]\[\int\limits_{0}^{4}\int\limits_{0}^{2} ye ^{-xy}( 4-0) dx dy\]\[\int\limits_{0}^{4}\int\limits_{0}^{2} ye ^{-xy}4dx dy\]

The second step is a little harder, but not by too much, since you are integrating only with respect to x and treating y as a constant. So try to remember how to integrate this. Remember, the derivative is the opposite direction of an integral so you can check your answer by taking the derivative if you're unsure, and of course I'll be here to check your answer.

Answer 8

Hmm, would you get -4y^2*e^(-xy) ?

Answer 9

Oops, never mind. I took the derivative instead.

Answer 10

Okay, I got -4e^(-xy)

Answer 11

@Kainui

Answer 12

Good, now evaluate it on the bounds.

Answer 13

-4e^(-2y) +4

Answer 14

Okay, I solved it. My final answer was 2e^(-8) + 14

Answer 15

Thanks for the help!

Answer 16

You're welcome! Glad I could help! =D