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Chapter 5: Q. 1 (page 493)
Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition with a graph or algebraic example, if possible.
The differential of a differentiable function u(x).
If u(x) is a differentiable function of x, then differential du is equal to
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Solve the integral:.
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)?
Solve the following two ways:
(a) with the substitution
(b) by completing the square and then applying the trigonometric substitution x + 2 = 2 sec u.
Which of the integrals that follow would be good candidates for trigonometric substitution? If a trigonometric substitution is a good strategy, name the substitution. If another method is a better strategy, explain that method.
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Solve the integral:.
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