Chapter 15.1, Problem 8E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

The contour map shows the temperature, in degrees Fahrenheit, at 4:00 pm on February 26. 2007, in Colorado. (The state measures 388 mi west to cast and 276 mi south to north.) Use the Midpoint Rule with *m = n =* 4 to estimate the average temperature in Colorado at that time.

To determine

**To estimate:** The average temperature of the Colorado state using midpoint rule.

Explanation

**Formula used:**

The double integral,

Where,
*l, b* are the length and breadth of each rectangle.

The given function is

The mid points of each rectangle is denoted by

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

The average value of a function *f* of two variables defined on *R* is,
*R*.

**Given:**

The measurement of the state is

The Riemann sum constants,

**Calculation:**

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

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

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