Chapter 5: Q. 37 (page 464)
Solvethe following two ways:
(a) with the substitution
(b) with the trigonometric substitution x = 2 tan u.
Short Answer
Part (a) The solution of the integral is
Part (b) The solution of the integral is
Chapter 5: Q. 37 (page 464)
Solvethe following two ways:
(a) with the substitution
(b) with the trigonometric substitution x = 2 tan u.
Part (a) The solution of the integral is
Part (b) The solution of the integral is
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Get started for freeComplete 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.
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.
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 ?
Domains and ranges of inverse trigonometric functions: For each function that follows, (a) list the domain and range, (b) sketch a labeled graph, and (c) discuss the domains and ranges in the context of the unit circle.
Solve the integral:.
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