10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

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 ∫01cosx1−xdx and approximate its value according to the trapezoidal rule.

The improper integral: ∫01cosx1−xdx.

The value of: u=1−x.

Formula used:

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

The integral will be:

∫abf(x)dx≈b−a2n[f(x0)+2f(x1)+2f(x2)+...2f(xn)]

Calculation:

As u=1−x,u2=1−x,2udu=−dx

Check out a sample textbook solution.

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Calculus

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

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Math
Calculus Calculus 10th Edition

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