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Chapter 5: Q 29. (page 495)
Convergence and divergence of basic improper integrals: Determine whether each of the given improper integrals converges or diverges. For those that converge, give the exact solution of the integral.
The integral is divergent for p>1.
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Solve given integrals by using polynomial long division to rewrite the integrand. This is one way that you can sometimes avoid using trigonometric substitution; moreover, sometimes it works when trigonometric substitution does not apply.
Solve the integral:.
Complete the square for each quadratic in Exercises 28鈥�33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.
For each function u(x) in Exercises 9鈥�12, write the differential du in terms of the differential dx.
Find three integrals in Exercises 21鈥�70 in which the denominator of the integrand is a good choice for a substitution u(x).
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