Find the region E for which the triple integral int int int E(1-x^2-2y^2-3z^2)dV. Is a maximum.

Leyla Bishop

Leyla Bishop

Open question

2022-08-17

Find the region E for which the triple integral
E(1x22y23z2)dV
Is a maximum.

Answer & Explanation

elverku7

elverku7

Beginner2022-08-18Added 9 answers

Remember that:
The points inside the ellipsoid x2+2y2+3z2=1 satisfy the Inequality
x2+2y2+3z21
That means the expression 1x22y23z2 is positive only when the point (x,y,z) is inside an ellipsoid.
Hence the maximum value of the Integral
E(1x22y23z2)dV
occurs when E is the region inside an ellipsoid.
Result:
E is the region inside the ellipsoid x2+2y2+3z2=1

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?