Chapter 5: Q 20. (page 495)
Defining improper integrals: Fill in the blanks, using limits and proper definite integrals to express each of the following types of improper integrals.
If f is a continuous on , then for any real number c,
Chapter 5: Q 20. (page 495)
Defining improper integrals: Fill in the blanks, using limits and proper definite integrals to express each of the following types of improper integrals.
If f is a continuous on , then for any real number c,
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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.)
Find three integrals in Exercises 27–70 for which a good strategy is to use integration by parts with and dv the remaining part.
Solve the integral
Solve each of the integrals in Exercises 39–74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
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.
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