Chapter 5: Q 10. (page 451)
Describe strategies for solving the types of integrals given.
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Short Answer
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Chapter 5: Q 10. (page 451)
Describe strategies for solving the types of integrals given.
odd
Take
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Get started for freeWhy 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 ?
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.
Explain why using trigonometric substitution with often involves a triangle with side lengths a and x and hypotenuse of length
For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
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.
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