Chapter 5: Q. 17 (page 464)
Why doesn’t the definite integral make sense? (Hint: Think about domains.)
Short Answer
Ans: is not defined in .
Chapter 5: Q. 17 (page 464)
Why doesn’t the definite integral make sense? (Hint: Think about domains.)
Ans: is not defined in .
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Get started for freeWhy don’t we need to have a square root involved in order to apply trigonometric substitution with the tangent? In other words, why can we use the substitution when we see , even though we can’t use the substitution unless the integrand involves the square root of? (Hint: Think about domains.)
Solve the integral: .
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.
Find three integrals in Exercises 27–70 for which either algebra or u-substitution is a better strategy than integration by parts.
Solve given integrals by using polynomial long division to rewrite the integrand. This is one way that you can sometimes avoid using trigonometric substitution; moreover, sometimes it works when trigonometric substitution does not apply.
dx
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