Math Help - Another Triple Integral

1. Another Triple Integral

Evaluate the triple integral where is the solid bounded by the paraboloid and .

Can someone help me on the setup, Thank you so much!

2. hopefully you know what the volume looks like... it's 'bowl' shaped.

integrate 1 over y and z first, i.e. integrate over the circle x = 8x^2 + 8y^2, where x is fixed. can you do this? then integrate these elements (which are functions of x) * x over x between 0 and 8...

to make thing simpler, use cylindrical coordinates.

3. I know how to integrate but I don't know how to setup the limits of integrations

4. Originally Posted by jffyx
Evaluate the triple integral where is the solid bounded by the paraboloid and .

Can someone help me on the setup, Thank you so much!
The solid has circular cross sections in the planes defined by $x=\sqrt{r}$ of radius $r$, and so of area $\pi r^2=\pi x$ , so our integral becomes:

$I=\int_{x=0}^8 \pi x^2 \ dx$

CB