Calculus, Single Variable: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134766850

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Question

Chapter 8.2, Problem 77E

To determine

To show: $∫f(x)g(x)dx=f(x)G1(x)−∫f′(x)G1(x)dx$

To determine

To show: $∫f(x)g(x)dx=f(x)G1(x)−f′(x)G2(x)+∫f″(x)G2(x)dx$

To determine

To write: The integral formula that results from three applications of integration by parts, and construct the associated tabular integration table.

To determine

To evaluate: The integral $∫x2e0.5xdx$ and find the required number of the row required in the table.

To determine

To evaluate: The integral $∫x3cosxdx$ by constructing an appropriate table: Explain the reason behind that the process terminates after four rows of the table have been filled in.

To determine

To explain: The tabular integration is particularly suited to integrals of the form $∫pn(x)g(x)dx$ .

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Chapter 8.2, Problem 76E

Chapter 8.2, Problem 78E

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Chapter 8 Solutions

Calculus, Single Variable: Early Transcendentals (3rd Edition)

Ch. 8.1 - What change of variable would you use for the...Ch. 8.1 - Prob. 2QC Ch. 8.1 - Prob. 3QC Ch. 8.1 - Prob. 4QC Ch. 8.1 - What change of variables would you use for the...Ch. 8.1 - Prob. 2E Ch. 8.1 - What trigonometric identity is useful in...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E

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∫ f ( x ) g ( x ) d x = f ( x ) G 1 ( x ) − ∫ f ′ ( x ) G 1 ( x ) d x

Solution Summary: The author explains how the required result is proved by using integration by parts.

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To show: $∫f(x)g(x)dx=f(x)G1(x)−∫f′(x)G1(x)dx$

To show: $∫f(x)g(x)dx=f(x)G1(x)−f′(x)G2(x)+∫f″(x)G2(x)dx$

To write: The integral formula that results from three applications of integration by parts, and construct the associated tabular integration table.

To evaluate: The integral $∫x2e0.5xdx$ and find the required number of the row required in the table.

To evaluate: The integral $∫x3cosxdx$ by constructing an appropriate table: Explain the reason behind that the process terminates after four rows of the table have been filled in.

To explain: The tabular integration is particularly suited to integrals of the form $∫pn(x)g(x)dx$ .

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Chapter 8 Solutions