Chapter 5: Q. 32 (page 478)
Use limits of definite integrals to calculate each of the improper integrals in Exercises.
Short Answer
The improper integral diverges.
Chapter 5: Q. 32 (page 478)
Use limits of definite integrals to calculate each of the improper integrals in Exercises.
The improper integral diverges.
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Get started for freeExplain why and are essentially the same integral after a change of variables.
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.
True/False: Determinewhethereachofthestatementsthat follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.
(a) True or False: is a proper rational function.
(b) True or False: Every improper rational function can be expressed as the sum of a polynomial and a proper rational function.
(c) True or False: After polynomial long division of p(x) by q(x), the remainder r(x) has a degree strictly less than the degree of q(x).
(d) True or False: Polynomial long division can be used to divide two polynomials of the same degree.
(e) True or False: If a rational function is improper, then polynomial long division must be applied before using the method of partial fractions.
(f) True or False: The partial-fraction decomposition of is of the form
(g) True or False: The partial-fraction decomposition of is of the form .
(h) True or False: Every quadratic function can be written in the form
Problem Zero: Read the section and make your own summary of the material.
Find three integrals in Exercises 21–70 in which the denominator of the integrand is a good choice for a substitution u(x).
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