Chapter 5: Q. 10 (page 428)
Find three integrals in Exercises 27–70 for which either algebra or u-substitution is a better strategy than integration by parts.
Short Answer
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Chapter 5: Q. 10 (page 428)
Find three integrals in Exercises 27–70 for which either algebra or u-substitution is a better strategy than integration by parts.
, ,
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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 how to know when to use the trigonometric substitutions , Describe the trigonometric identity and the triangle that will be needed in each case. What are the possible values for and in each case?
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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