Chapter 15, Problem 59RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Suppose that *f* is continuous on a disk that contains the point (*a*, *b*)*.* Let *D _{r}* be the closed disk with center (

To determine

**To prove:** The given statement

Explanation

**Given:**

The function *f* is a continuous function on a disk *D* that contains the point

*r.*

**Formula used:**

**The Mean value theorem:**

If *f* is a continuous function on a plane region *D* that is of type 1 or 2, then there exists a point *D* such that

**Proof:**

From the mean value theorem mentioned above, it is observed that *r.* So, the area of the region is given by

From the above equation, it is enough to show that

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