   Chapter 6.3, Problem 35E ### 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
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# Error Analysis In Exercises 33-36, 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. Let n = 4. ∫ 0 1 e x 3 d x

(a)

To determine

To calculate: The bounds for the error in approximation for the integral 01ex3dx with the Trapezoidal Rule by using Error formula.

Explanation

Given Information:

The definite integral is 01ex3dx, and n=4

Formula used:

Errors in Trapezoidal Rule:

If a function f is continuous on [a,b], then the errors E in approximating,

abf(x)dx

As shown below,

|E|(ba)312n2[max|f(x)|], axb

Calculation:

Calculation to get error in the approximation of the integral:

Consider the definite integral 01ex3dx.

The double derivative of the f(x)=ex3.

First derivative of f(x)=ex3

f(x)=3x2ex3

Second derivative of f(x)=ex3,

(b)

To determine

To calculate: The bounds for the error in approximation for the integral 01ex3dx with the Simpson’s Rule by using Error formula.

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