Chapter 5: Q. 9 (page 477)
Why does it make sense that diverges when ? Consider how compares with in this case.
Short Answer
For ,is greater than in the interval , whose improper integral on is known to diverge.
Chapter 5: Q. 9 (page 477)
Why does it make sense that diverges when ? Consider how compares with in this case.
For ,is greater than in the interval , whose improper integral on is known to diverge.
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Get started for freeSolve 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.
dx
Suppose v(x) is a function of x. Explain why the integral
of dv is equal to v (up to a constant).
Explain how to use long division to write the improper fraction as the sum of an integer and a proper fraction.
Solve the integral:.
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