Another Triple Integral

**jffyx** · April 22nd 2009, 02:17 AM

Evaluate the triple integral

where

is the solid bounded by the paraboloid

and

.

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

**treolor478** · April 22nd 2009, 03:12 AM

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.

**jffyx** · April 22nd 2009, 03:29 AM

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

**CaptainBlack** · April 24th 2009, 08:04 AM

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

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