Optimizing Paraboloid Bounds for Triple Integral

[Larrytsai]

Homework Statement

Evaluate the triple integral xdV where E is the solid bounded by the paraboloid x= 2y^2 + 2z^2 and x=2.

The Attempt at a Solution

The bounds I got are

for z

-sqrt(1-y^2) <= y <= sqrt(1-y^2)

for y

-1 <= y <= 1

for x

2y^2 + 2z^2 <= x <= 2

are these correct?

 

[benorin]

$$\iiint{2y^2+2z^2\leq x\leq 2}xdV= \iint_{y^2+z^2\leq 1}\int_{2y^2+2z^2}^{2}x\,dxdA$$

 

[Larrytsai]

Im sorry I don't quite understand what you have written, can you please explain if possible?