Chapter 5: Q. 20 (page 477)
Express each improper integral in Exercises15–20 as a sum of limits of proper definite integrals. Do not calculate any integrals or limits; just write them down.
Short Answer
The integral is,
Chapter 5: Q. 20 (page 477)
Express each improper integral in Exercises15–20 as a sum of limits of proper definite integrals. Do not calculate any integrals or limits; just write them down.
The integral is,
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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.
Which of the integrals that follow would be good candidates for trigonometric substitution? If a trigonometric substitution is a good strategy, name the substitution. If another method is a better strategy, explain that method.
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Consider the integral .
(a) Solve this integral by using u-substitution.
(b) Solve the integral another way, using algebra to multiply out the integrand first.
(c) How must your two answers be related? Use algebra to prove this relationship.
Show by differentiating (and then using algebra) that and are both antiderivatives of . How can these two very different-looking functions be an antiderivative of the same function?
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