Triple Integrals: Evaluating ∫∫∫6xydV

[bodensee9]

Homework Statement

Can someone see if I have set this up correctly? So I am to evaluate ∫∫∫6xydV. The region lies between z = 1+x+y and above the region in the xy plane bounded by the curves y = √x, y = 0, x = 1.
So, would this be equal to ∫∫∫6xydzdydx, where z is evaluated from 0 to 1+x+y, y is evaluated from √x to -1-x, and x is evaluated from 0 to 1? Thanks!

Homework Equations

The Attempt at a Solution

 

[P3X-018]

Your limits for z and x looks fine, but why do you think y goes from \sqrt{x} to -x-1? Where do you get that last mentioned limit for y?

 

[bodensee9]

I guess because that's where the projection of z = 1+x+y on the xy plane intersects the curve y = √x. so i thought y would range between √x and -1 - x. Thanks.