Chapter 5: Q. 3 (page 441)
What is a rational function? What does it mean for a rational function to be proper? Improper?
Short Answer
The function that can be expressed as a quotient of polyomial.
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Chapter 5: Q. 3 (page 441)
What is a rational function? What does it mean for a rational function to be proper? Improper?
The function that can be expressed as a quotient of polyomial.
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Solve the integral
Solvethe following two ways:
(a) with the substitution
(b) with the trigonometric substitution x = 2 tan u.
List some things which would suggest that a certain substitution u(x) could be a useful choice. What do you look for when choosing u(x)?
Explain why, if , then is if and is if . Your explanation should include a discussion of domains and absolute values.
Solve the integral:
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