Chapter 5: Q. 75 (page 452)
Solve each of the definite integrals in Exercises 67–76.
.
Short Answer
The answer is.
Chapter 5: Q. 75 (page 452)
Solve each of the definite integrals in Exercises 67–76.
.
The answer is.
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Get started for freeFind three integrals in Exercises 21–70 that we can anti-differentiate immediately after algebraic simplification.
Solve given definite 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.
Complete the square for each quadratic in Exercises 28–33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.
Explain why using trigonometric substitution with often involves a triangle with side lengths a and x and hypotenuse of length
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