   Chapter 6, Problem 11TYS ### 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

# Use Simpson’s Rule with n   = 4 to approximate ∫ 2 5 ( x 2 − 2 x )   d x .Compare your result with the exact value of the definite integral.

To determine

To calculate: The approximate value of 25(x22x)dx using the Trapezoidal Rule with n=4 and compare the result with the exact value of the definite integral.

Explanation

Given Information:

The definite integral is 25(x22x)dx,n=4.

Formula used:

Trapezoidal Rule:

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

abf(x)dx=(ba2n)[f(x0)+2f(x1)++2f(xn1)+f(xn)]

Calculation:

Calculation to get exact value:

Consider the definite integral 25(x22x)dx.

25(x22x)dx=[x332x22]25=[x33x2]25=13(5)3(5)213(2)3+(2)2=13×1252583+4

Simplify as:

25(x22x)dx=125758+123=137833=543=18

Therefore, the exact value of the integral is 18.

Calculation by Trapezoidal Rule:

Consider the definite integral 25(x22x)dx

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