   Chapter 13.8, Problem 15E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 13-18, approximate each integral by(a) the Trapezoidal Rule.(b) Simpson’s Rule.Use n = 4 and round answers to three decimal places. ∫ 1 0   e − x 2 d x

(a)

To determine

To calculate: The approximate value of 01ex2dx for n=4 by Trapezoidal Rule.

Explanation

Given information:

The provided integral is 01ex2dx for n=4.

Formula used:

The length of each n subdivision for a closed interval [a,b].

h=ban

The approximate value of integral abf(x)dx for n equal subdivision of closed interval [a,b] by Trapezoidal Rule is,

abf(x)dxh2[f(x0)+2f(x1)+2f(x2)+2f(x3)++f(xn)]

Where h is the length of each subdivision.

Calculation:

Consider the provided integral 01ex2dx for n=4.

Since the number of equal subdivision is 4 and the lower and upper limit of the integral are 0 and 1 respectively.

n=4a=0b=1

Use the formula for the length of each n subdivision for a closed interval [a,b].

h=ban

Substitute 0 for a, 1 for b and 4 for n.

h=104h=14

The corresponding value of xi=a+ih and f(xi)=xi2 for a=0 and h=14 is shown below

(b)

To determine

To calculate: The approximate value of 01ex2dx for n=4 by Simpson Rule.

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