Explore BrainMass

# Integration : Fubini's Theorem

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Use attached to solve the following question by integrating over an appropriate rectangle.

Assume f is class C2 Prove the following theorem by Fubini's Theorem.

For f of class C2

Left Hand side:

Right Hand side:

Use above to solve the following question by integrating over an appropriate rectangle.

Assume f is class C2 Prove the following theorem by Fubini's Theorem.
Theorem:
Let be open and suppose f: is a class C2 function.
Then for any i and j we have

(Hint: Proceed by contradiction if the mixed partials are not equal at some point, apply (a) to show we can find a rectangle on which, )
(a) Suppose is open and f: is continuous. If a and f(a) >0. there is &#948;>0 so that f(x) > 0 for all )

https://brainmass.com/math/integrals/integration-fubinis-theorem-31024

#### Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Left Hand side:
(*)
Right ...

#### Solution Summary

An integral is found using Fubini's theorem.

\$2.49