Chapter 5.5, Problem 12E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

(a) Find the average value of f on the given interval.

(b) Find c such that

(c) Sketch the graph of f and a rectangle whose area is the same as the area under the graph of f.

To determine

**(a)**

**To find:**

The average value of

Explanation

**1) Concept:**

Use the formula for the average value of

**2) Formula:**

**3) Given:**

**4) Calculation:**

Here,

Substituting all the above in the formula,

Simplify.

Here, we need to use the substitution method.

Let

Since this is a definite integral, the limits also change with respect to the substitution.

When

Substituting all in the above integration,

To determine

**(b)**

**To find:**

The value of

To determine

**(c)**

**To sketch:**

The graph of

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