   Chapter 6.3, Problem 2CP ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Checkpoint 2Use Simpson’s Rule with n = 4 to approximate ∫ 0 1 e 2 x d x .

To determine

The approximate value of the integral 01e2xdx for n=4 by Simpsons Rule.

Explanation

Given Information:

The definite integral is 01e2xdx,n=4

Formula used:

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

abf(x)dx(ba3n)[f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(x4)++f(xn)]

Calculation:

Consider the definite integral 01e2xdx.

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

The width of each subinterval is,

104=14

The end points of subintervals for the calculated width,

x0=0,x1=14,x2=12,x3=34,x4=1

The value function f(xi)=xi2 for corresponding width is shown below

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