Compute the volume of the region that lies behind the plane and

[khfrekek92]

Homework Statement

compute the volume of the region that lies behind the plane x+y+z=8 and in front of the region in the yz-plane that is bounded by z=(3/2)sqrt(y) and z=(3/4)y

Homework Equations

double/triple integral?

The Attempt at a Solution

I've graphed it but I don't know what to integrate, or the boundaries.. any help would be much appreciated!

 

[lineintegral1]

It may be useful to do a triple integral here. Recall that your boundary regions are defined by the regions defined in the problem. You want to solve for the forward/backward endpoints on x, the left/right endpoints on y, and the upward/downward endpoints on z. Remember that some limits of integration may be functions of one or more variable. Try to decide which variable it may be most convenient to integrate with respect to first. For instance, maybe the order of integration is most efficiently done on dxdzdy. Maybe it's another order. Try to figure this out and we'll see if we can help you further.

 

[khfrekek92]

Perfect! I got it all figured out, thank you so much for your help!