Chapter 5: Q 35. (page 429)
Solve the integral:
Short Answer
The required answer is.
Chapter 5: Q 35. (page 429)
Solve the integral:
The required answer is.
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Get started for freeSuppose 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
True/False: Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.
(a) True or False: The substitution x = 2 sec u is a suitable choice for solving.
(b) True or False: The substitution x = 2 sec u is a suitable choice for solving.
(c) True or False: The substitution x = 2 tan u is a suitable choice for solving
(d) True or False: The substitution x = 2 sin u is a suitable choice for solving
(e) True or False: Trigonometric substitution is a useful strategy for solving any integral that involves an expression of the form .
(f) True or False: Trigonometric substitution doesn’t solve an integral; rather, it helps you rewrite integrals as ones that are easier to solve by other methods.
(g) True or False: When using trigonometric substitution with , we must consider the cases and separately.
(h) True or False: When using trigonometric substitution with , we must consider the cases and separately.
Why is it okay to use a triangle without thinking about the unit circle when simplifying expressions that result from a trigonometric substitution withor ? Why do we need to think about the unit circle after trigonometric substitution with ?
For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
What is a rational function? What does it mean for a rational function to be proper? Improper?
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