Chapter 15.1, Problem 7E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

A contour map is shown for a function *f* on the square *R =* [0, 4] × [0. 4].

(a) Use the Midpoint Rule with *m* = *n =* 2 to estimate the value of
*.*

(b) Estimate the average value of *f*.

(a)

To determine

**To estimate:** The value of given double integral over the rectangle *R* by using midpoint rule.

Explanation

**Formula used:**

The double integral,

Where,
*a* is the side of each square.

The given function is

The mid points of each rectangle is denoted by

The Riemann sum constants are denoted by *m*, *n*.

**Given:**

The rectangular region,

The Riemann sum constants,

**Calculation:**

Plot the given rectangle in the graph and pick the mid points of each rectangle.

From Figure 1, it is observed that the mid points of each rectangle is

(b)

To determine

**To estimate:** The average value of given function.

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