Chapter 5: Q. 40 (page 478)
Use limits of definite integrals to calculate each of the improper integrals in Exercises.
Short Answer
The value of the integral is
Chapter 5: Q. 40 (page 478)
Use limits of definite integrals to calculate each of the improper integrals in Exercises.
The value of the integral is
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Get started for freeFind three integrals in Exercises 39–74 that can be solved without using trigonometric substitution.
Solve the following two ways:
(a) with the trigonometric substitution x = 3 tan u;
(b) with algebra and the derivative of the arctangent.
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.
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.
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.
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