Triple integral, 2 parabolic cylinders

[EV33]

Homework Statement

Find the volume of the region which is bounded by the parabolic cylinders y=x², x=y² and z=x+y and z=0

Homework Equations

The Attempt at a Solution

I solved x=y² for y, and set that equal to y=x², and I got the intersection of the two parabolic cylinders to be at x=1. So I set it up as follows

∫∫∫ dzdydx R={(x,y,z)l 0<x<1,x²<y<sqrt(x), 0<Z<x+y}

(Preted my < are actually < and equal to signs)

I was wondering if someone could tell me if my set up is correct.

Thank you.

 

[HallsofIvy]

Yes, that's exactly right.

By the way, "LaTex" is much nicer. On this board
[ tex ]\int_{z=0}^{x+y}\int_{y=x^2}^{\sqrt{x}}\int_{x= 0}^1 dxdydz [ /tex ]
gives (without the spaces inside [ ])
$$\int_{z=0}^{x+y}\int_{y=x^2}^{\sqrt{x}}\int_{x= 0}^1 dxdydz$$

Some other boards use " " or "\( \)" or other things as delimiters but the codes are the same.

 

[EV33]

Ok I will try that next time. Thank you so much.