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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Get started for freeExplain why using trigonometric substitution with often involves a triangle with side lengths a and x and hypotenuse of length
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?
Suppose . Calculate and compare the values of the following definite integrals:
role="math" localid="1648786835678"
Consider the integral .
(a) Solve this integral by using u-substitution with and .
(b) Solve the integral another way, using u-substitution with and .
(c) How must your two answers be related? Use algebra to prove this relationship.
Solve given definite integral.
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