Triple Integrals: Finding Mass of a Bounded Solid

[theBEAST]

Homework Statement

Find the mass of a solid of constant density that is bounded by the parabolic cylinder x=y² and the planes x=z, z=0, and x=1.

The Attempt at a Solution

https://dl.dropbox.com/u/64325990/Photobook/Photo%202012-06-07%202%2033%2024%20PM.jpg

I first drew some diagrams to help me visualize the problem and then I tried to solve this integral but it ended up to be in terms of x. What am I doing wrong?

 

[algebrat]

If you want to integrate in the order x, then y then z, then...

For an arbitrary (y,z), x should go from the z=x plane to the x=1 plane,
that is, x=z..1.

For an arbitrary z, y should go from -√x to √x.

Then z should go from 0 to 1.

So your last limit should not be a function of x, nor y.You may want to draw all surfaces in one 3d pic. so you can see that the lower limit in x should have been x=z, not x=y^2.
You may want to consider othe orders of integration, so that you avoid the square roots.

 

[SammyS]

Homework Statement

Find the mass of a solid of constant density that is bounded by the parabolic cylinder x=y² and the planes x=z, z=0, and x=1.

The Attempt at a Solution

https://dl.dropbox.com/u/64325990/Photobook/Photo%202012-06-07%202%2033%2024%20PM.jpg

I first drew some diagrams to help me visualize the problem and then I tried to solve this integral but it ended up to be in terms of x. What am I doing wrong?

If you integrate w.r.t. x first (inner integral)n then there shouldn't any x in the limits of the outer two integrals.