# Maximum of a triple integral

## Homework Statement

Find the region E for which the triple integral:

(triple integral over E) (1 - x^2 -2y^2 -3z^2) dV is a maximum.

## The Attempt at a Solution

I remember in earlier math courses finding the derivative of a single variable integral, does this problem involve finding the derivative of a triple integral and setting it equal to zero to find the maximum? If so, how would you do that?

## Answers and Replies

tiny-tim
Science Advisor
Homework Helper
Hi phrygian! You're making this too complicated …

any region in which the integrand is positive will increase the integral, and any region in which the integrand is negative will decrease it …

soooo … ? HallsofIvy
Science Advisor
Homework Helper
In other words, where is $1 - x^2 -2y^2 -3z^2\ge 0$?

So the region is when z = sqrt( (-2y^2 - x^2)/3 )? Is this a complete answer how do you describe the region?

tiny-tim
Science Advisor
Homework Helper
Hi phrygian! (have a square-root: √ and try using the X2 tag just above the Reply box )
So the region is when z = sqrt( (-2y^2 - x^2)/3 )? Is this a complete answer how do you describe the region?

erm … you can't have √ of a negative nnumber, can you? Try again. 