Find the triple integral of xy

[magnifik]

find the triple integral of xy where E is bounded by y = x^2 and x = y^2 and the planes z = 0 and z = x + y.

i got 1/3 as a solution, but I'm not sure if i did it right, specifically the part in finding the boundaries for x and y. i found that they intersected at (0,0) and (1,1) so i had the region
[0,1] x [0,1] x [0,x+y] then evaluated the triple integral dzdydx. did i take the right approach?

 

[vela]

Your limits for the second integral are incorrect. If your outside integral is with respect to x, the limits of the middle integral should be the upper and lower limits of y for a constant value of x.

 

[magnifik]

Your limits for the second integral are incorrect. If your outside integral is with respect to x, the limits of the middle integral should be the upper and lower limits of y for a constant value of x.

is the boundary 0 to x^2?

 

[vela]

No. Graph the functions on the xy-plane.

 

[magnifik]

since it's only in the first quadrant the lower bound should be x^2 and upper bound should be sqrt(x)?

 

[vela]

Yup, that's right.