   Chapter 8.8, Problem 106E

Chapter
Section
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: 01cosx1xdx.

The value of: u=1x.

Formula used:

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

The integral will be:

abf(x)dxba2n[f(x0)+2f(x1)+2f(x2)+...2f(xn)]

Calculation:

As u=1x,u2=1x,2udu=dx

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