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 freeExplain why using trigonometric substitution with often involves a triangle with side lengths a and x and hypotenuse of length
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.
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?
Explain how to use long division to write the improper fraction as the sum of an integer and a proper fraction.
Find three integrals in Exercises 39–74 that can be solved by using a trigonometric substitution of the form .
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