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Chapter 5: Q. 9 (page 428)

Explain why choosing $u = 1$ (and thus choosing dv to be the entire integrand, including dx) is never a good choice for integration by parts.

Short Answer

Expert verified

Hence proved.

Step by step solution

01

Step 1. Explanation.

Choosing $u = 1$ , is never a good choice for integration by parts because if $u = 1$ , then Integrating $d v i s$ equivalent to solving the original integral.

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Most popular questions from this chapter

Find three integrals in Exercises 27–70 for which a good strategy is to apply integration by parts twice.

Solve the integral $\int x^{3} \sqrt{x^{2} - 1} d x$ three ways:

(a) with the substitution $u = x^{2} - 1,$ followed by back substitution;

(b) with integration by parts, choosing localid="1648814744993" $u = x^{2} and d v = x \sqrt{x^{2} - 1} d x;$

(c) with the trigonometric substitution x = sec u.

Solve the integral: $\int x^{2} \cos x d x$ .

Solve the integral: $\int \frac{x}{e^{x}} d x$

Find three integrals in Exercises 39–74 that can be solved by using a trigonometric substitution of the form $x = a \tan u$ .

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