Chapter 5: Q. 19 (page 464)
Find three integrals in Exercises 39–74 that can be solved without using trigonometric substitution.
Short Answer
Ans:
Chapter 5: Q. 19 (page 464)
Find three integrals in Exercises 39–74 that can be solved without using trigonometric substitution.
Ans:
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Get started for freeTrue/False: Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.
(a) True or False: The substitution x = 2 sec u is a suitable choice for solving
(b) True or False: The substitution x = 2 sec u is a suitable choice for solving
(c) True or False: The substitution x = 2 tan u is a suitable choice for solving
(d) True or False: The substitution x = 2 sin u is a suitable choice for solving
(e) True or False: Trigonometric substitution is a useful strategy for solving any integral that involves an expression of the form
(f) True or False: Trigonometric substitution doesn’t solve an integral; rather, it helps you rewrite integrals as ones that are easier to solve by other methods.
(g) True or False: When using trigonometric substitution with
(h) True or False: When using trigonometric substitution with
For each integral in Exercises 5–8, write down three integrals that will have that form after a substitution of variables.
For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
Solve the integral
Explain why it makes sense to try the trigonometric substitution
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