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7th Edition

James Stewart + 2 others

Publisher: Brooks Cole

ISBN: 9781305071759

Chapter 13.5, Problem 8E

Textbook Problem

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**Estimating Areas Using Rectangles** Approximate the area of the shaded region under the graph of the given function by using the indicated rectangles. (The rectangles have equal width.)

**8.** *f*(*x*) = 9*x* − *x*^{3}

To determine

**To Find:** The approximate area under the function

**Given:**

The given function is,

**Calculation:**

Divide the area under the given function into four small rectangles as shown in Figure (1) below.

Figure (1)

The total area under the given function is sum of areas of individual rectangles.

The total area under the function is,

Use summation and write equation (1) as,

Here,

The width of each rectangle is given by,

Here, *b* and *a* are end points of required area, *n* is number of rectangles.

The end points *a* and *b* as shown in Figure (1) are

Calculate width of each rectangle, substitute
*n*,
*b* and
*a* in

Calculate height

Height of second rectangle

Height of third rectangle

Precalculus: Mathematics for Calculus (Standalone Book)

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