How do you find the maximum for a triple integral without using a prefix?

[phrygian]

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.

Homework Equations

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!

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]

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!

(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. ​