Chapter 5: Q. 19 (page 491)
Verify that the formula in Theorem 5.28 is true in the case
whereandrole="math" localid="1649347279693"
Short Answer
When, , role="math" localid="1649570449613" and which verifies the formula.
Chapter 5: Q. 19 (page 491)
Verify that the formula in Theorem 5.28 is true in the case
whereandrole="math" localid="1649347279693"
When, , role="math" localid="1649570449613" and which verifies the formula.
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Get started for freeFor each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
For each integral in Exercises 5–8, write down three integrals that will have that form after a substitution of variables.
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 integral:
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