Chapter 15, Problem 12P

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate

To determine

**To evaluate:** The value of

Explanation

**Formula used:**

The Riemann sum can be expressed as,

Here,

The sample points of the upper right corner of each square is denoted by

The image value of the sample points under the function

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

**Calculation:**

Rewrite the given summation as follows.

Since, the denominator root contains

Since, *x is* denoted by *R* is divided into *n* subintervals on the *x-*axis. Similarly, since, *y is* denoted by *R* is divided into *y-*axis. Take the sample points anywhere from the sub rectangle. The area of each sub rectangle is given by,

Thus when

Use the formula mentioned above to integrate it

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