triple integral volumes

mathstresser

Junior Member
Joined
Jan 28, 2006
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134
Evaluate the triple integral

\(\displaystyle \L\\\int_{v}^{v}\int_{v}^{v}\int_{v}^{v}xdV\),
where it is bounded by the paraboloid \(\displaystyle \L\\ x=4y^2+4z^2\)
and the plane x=4.

I think my only problem is figuring out the intervals.

I was thinking

\(\displaystyle \L\\\int_{0}^{4}\int_{v}^{v}\int_{v}^{v}xdydzdx\)

So, then I thought the intervals on the y and z axes should be

\(\displaystyle \L\\\ -sqrt(.25x-y^2)<=z<=sqrt(.25x-y^2)\)
\(\displaystyle \L\\\ -sqrt(.25x-z^2)<=y<=sqrt(.25x-z^2)\)

But those intervals for y and z don't work.

What am I doing wrong?
 
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