mathstresser
Junior Member
- Joined
- Jan 28, 2006
- Messages
- 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?
\(\displaystyle \L\\\int_{v}^{v}\int_{v}^{v}\int_{v}^{v}xdV\),
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?