Chapter 5: Q. 84 (page 465)
Solve given definite integral.
Chapter 5: Q. 84 (page 465)
Solve given definite integral.
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Show by differentiating (and then using algebra) that and are both antiderivatives of . How can these two very different-looking functions be an antiderivative of the same function?
Suppose you use polynomial long division to divide p(x) by q(x), and after doing your calculations you end up with the polynomial as the quotient above the top line, and the polynomial 3x − 1 at the bottom as the remainder. Then
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.
For each integral in Exercises 5–8, write down three integrals that will have that form after a substitution of variables.
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