Maximum of a triple integral

[phrygian]

1. The problem statement, all variables and given/known data

Find the region E for which the triple integral:

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

2. Relevant equations



3. 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?

[tiny-tim]

Hi phrygian! :smile:

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 … ? :wink:

[HallsofIvy]

In other words, where is 1 - x^2 -2y^2 -3z^2\ge 0?

[phrygian]

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]

Hi phrygian! :smile:

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

erm :redface: … you can't have √ of a negative nnumber, can you? :wink:

Try again. :smile: