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.
All the tools & learning materials you need for study success - in one app.
Get started for freeSuppose v(x) is a function of x. Explain why the integral
of dv is equal to v (up to a constant).
Suppose you use polynomial long division to divide p(x) by q(x), and after doing your calculations you end up with the polynomial as the quotient above the top line, and the polynomial 3x − 1 at the bottom as the remainder. Then
Solve the following two ways:
(a) with the substitution
(b) by completing the square and then applying the trigonometric substitution x + 2 = 2 sec u.
For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
Solve the integral :
What do you think about this solution?
We value your feedback to improve our textbook solutions.