Chapter 5: Q 2. (page 495)
Use Pythagorean identities to rewrite each of the following trigonometric expressions.
Short Answer
The obtained result is.
Chapter 5: Q 2. (page 495)
Use Pythagorean identities to rewrite each of the following trigonometric expressions.
The obtained result is.
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Get started for freeFind three integrals in Exercises 21โ70 in which the denominator of the integrand is a good choice for a substitution u(x).
Solve each of the integrals in Exercises 39โ74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
Consider the integral .
(a) Solve this integral by using u-substitution with and .
(b) Solve the integral another way, using u-substitution with and .
(c) How must your two answers be related? Use algebra to prove this relationship.
Why doesnโt the definite integral make sense? (Hint: Think about domains.)
Complete the square for each quadratic in Exercises 28โ33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.
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