Chapter 5: Q. 37 (page 464)
Solvethe following two ways:
(a) with the substitution
(b) with the trigonometric substitution x = 2 tan u.
Short Answer
Part (a) The solution of the integral is
Part (b) The solution of the integral is
Chapter 5: Q. 37 (page 464)
Solvethe following two ways:
(a) with the substitution
(b) with the trigonometric substitution x = 2 tan u.
Part (a) The solution of the integral is
Part (b) The solution of the integral is
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Get started for freeExplain why and are essentially the same integral after a change of variables.
Solve given definite integral.
Solve the integral:
True/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.
Solve the following two ways:
(a) with the substitution
(b) by completing the square and then applying the trigonometric substitution x + 2 = 2 sec u.
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