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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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Using the Trapezoidal Rule and Simpson’s Rule In Exercises 41–46, approximate the value of the definite integral using (a) the Trapezoidal Rule and (b) Simpson’s Rule for the indicated value of n. Round your answers to three decimal places.

1 1 e x 4 d x , n = 4

(a)

To determine

To calculate: The value of the integral 11ex4dx,n=4 by using the Trapezoidal Rule and to approximate the value of the definite integral for the indicated value of n. Round your answers to three decimal places.

Explanation

Given Information:

The definite integral is 11ex4dx,n=4.

Formula used:

Trapezoidal Rule:

If a function f is continuous on [a,b], then

02f(x)dx,n=(ba2n)[f(x0)+2f(x0)+...+2f(xn1)+f(xn)]

Calculation:

Calculation by Trapezoidal Rule:

Consider the definite integral 11ex4dx,n=4.

When n=4, the width of each subinterval is

1(1)4=1+14=24=12

And the end points of subintervals are as follows:

At n=0,

x0=1

At n=1,

x1=1+12=2+12=12=0

(b)

To determine

To calculate: The value of the integral 11ex4dx,n=4 by using the Simpson’s Rule and to approximate the value of the definite integral for the indicated value of n. Round your answers to three decimal places.

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