Chapter 5: Q. 48 (page 417)
Solve each of the integrals in Exercises 21–70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)
Short Answer
The solution of the given integral is .
Chapter 5: Q. 48 (page 417)
Solve each of the integrals in Exercises 21–70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)
The solution of the given integral is .
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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 , we must consider the cases and separately.
(h) True or False: When using trigonometric substitution with , we must consider the cases and separately.
Find three integrals in Exercises 39–74 that can be solved without using trigonometric substitution.
Describe two ways in which the long-division algorithm for polynomials is similar to the long-division algorithm for integers and then two ways in which the two algorithms are different.
Solve the integral:
Suppose you use polynomial long division to divide p(x) by q(x), and after doing your calculations you end up with the polynomial as the quotient above the top line, and the polynomial 3x − 1 at the bottom as the remainder. Then
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