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Chapter 8.8, Problem 106E
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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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Chapter
Section
BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

u -Substitution In Exercises 105 and 106, rewrite the improper integral as a proper integral using the given u -substitution. Then use the Trapezoidal Rule with n = 5 to approximate the integral. ∫ 0 1 cos x 1 − x d x ,   u = 1 − x

To determine

To calculate: The proper integral from the improper integral 01cosx1xdx and approximate its value according to the trapezoidal rule.

Explanation

Given:

The improper integral: âˆ«01cosx1âˆ’xdx.

The value of: u=1âˆ’x.

Formula used:

The trapezoidal rule states that, let f be continuous on [a,b], then on approximation.

The integral will be:

âˆ«abf(x)dxâ‰ˆbâˆ’a2n[f(x0)+2f(x1)+2f(x2)+...2f(xn)]

Calculation:

As u=1âˆ’x,u2=1âˆ’x,2udu=âˆ’dx

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