Chapter 5.6, Problem 19E

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10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

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**Using the Midpoint Rule** In Exercises 15-20, use the Midpoint Rule with *n =* 4 to approximate the area of the region bounded by the graph of *f* and the x-axis over the interval. Sketch the region. *See Examples 2 and 3.*

Function |
Interval |

To determine

**To calculate:** The area bounded by the function *f* and *x*-axis.

Explanation

**Given Information:**

The provided function is

**Formula used:**

The approximate area of any definite integral

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

*n* is the subinterval value. and

Step2: by the use of above calculated value of 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;

Now, put *n* equal to 4,

Width

So, the interval

Now, the value of midpoint of each sub interval is calculated as;

for subinterval

For subinterval

For subinterval

For subinterval

So, the mid points of sub intervals are

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