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Chapter 5: Q 9. (page 451)
Describe strategy for solving the type of integral given.
is even.
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Suppose . Calculate and compare the values of the following definite integrals:
role="math" localid="1648786835678"
Solve the following two ways:
(a) with the substitution
(b) with the trigonometric substitution x = tan u.
Solve the integral:
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
Find three integrals in Exercises 27鈥�70 for which a good strategy is to use integration by parts with and dv the remaining part.
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