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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Error Analysis In Exercises 47 and 48, use the error formulas to find bounds for the error in approximating the definite integral using (a) the Trapezoidal Rule and (b) Simpson’s Rule for the indicated value of n.

0 1 e 3 x d x , n = 4

(a)

To determine

To calculate: The error in approximating the definite integral 01e3xdx,n=4 using the error formula of Trapezoidal Rule.

Explanation

Given Information:

The definite integral is 01e3xdx,n=4.

Formula used:

According to Trapezoidal Rule the error E in approximating abf(x)dx is as shown,

|E|(ba)312n2[max|f(x)|],axb

Calculation:

Consider the definite integral 01e3xdx,n=4.

Steps to determine the error, are as follows:

(1) Begin by finding the second derivative of f(x)=e3x.

f(x)=e3xf1(x)=3e3xf2(x)=9e3x

(2) Find the maximum of |f2(x)| on the interval [a,b]

(b)

To determine

To calculate: The error in approximating the definite integral 01e3xdx,n=4 using the error formula of Simpson’s Rule.

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