Chapter 13.8, Problem 10E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

For each integral in Problems 7-12, do the following.

(a) Approximate its value using the Trapezoidal Rule.

(b) Approximate its value using Simpson’s Rule.

(c) Find its exact value by integration.

(d) State which approximation is more accurate. (Round each result to 2 decimal places.)

**(a)**

To determine

**To calculate:** The approximate value of integral

Explanation

**Given information:**

The provided integral

**Formula used:**

The length of each *n* subdivision for a closed interval

The approximate value of integral

Where *h* is the length of each subdivision.

**Calculation:**

Consider the provided integral

Since the number of equal subdivision is 6 and the lower and upper limit of the integral are 1 and 4 respectively.

Use the formula for the length of each *n* subdivision for a closed interval

Substitute 1 for *a*, 4 for *b* and 6 for *n*.

The corresponding value of

**(b)**

To determine

**To calculate:** The approximate value of integral

**(c)**

To determine

**To calculate:** The exact value of

**(d)**

To determine

The most accurate approximation rule among the Trapezoidal rule and Simpson Rule.

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