Chapter 5: Q 43. (page 429)
Solve the integral:
The required answer is .
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
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.
Why don’t we ever have cause to use the trigonometric substitution ?
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.
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:.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
