Use the fact that a continuous function on a closed bounded domain D attains both a minimum

Question:

Use the fact that a continuous function on a closed bounded domain D attains both a minimum value m and a maximum value M, together with Theorem 3, to prove that the average value J lies between m and M. Then use the IVT in Exercise 68 to prove the Mean Value Theorem for Double Integrals.

THEOREM 3 Let f(x, y) and g(x, y) be integrable functions on D. (a) If f(x,y)  g(x, y) for all (x, y) e D,

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  answer-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

Question Posted: