Chapter 5: Q 45. (page 429)
Solve the integral:
Short Answer
The required answer is.
Chapter 5: Q 45. (page 429)
Solve the integral:
The required answer is.
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Get started for freeExplain why, if , then is if and is if . Your explanation should include a discussion of domains and absolute values.
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.
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
Solve the integral:
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