Chapter 5.6, Problem 4E

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10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

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**Approximating the Area of a Plane Region** In Exercises 1-6, use the rectangles to approximate the area of the region. Compare your result with the exact area obtained using a definite integral. See *Example 1.*

To determine

**To calculate:** The area bounded by the function

Explanation

**Given Information:**

The provided function is

**Formula used:**

The approximate area of any definite integral

Step1: First divide the provided interval of the function into *n* sub intervals by the use of formula;

Step2: Use above subinterval find the midpoint of each sub interval.

Step3: Final step is to obtain approximate area by calculating function *f* at each mid-point from the use of formula;

**Calculation:**

Consider the provided function

In provided graph, interval

Now, put

Width

So, the interval

Now, the value of midpoint of each rectangle is calculated as;

So, for first rectangle

Similarly, for second rectangle

For third rectangle

For last rectangle

So, the mid points of all four rectangles are

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