미분적분학 6장 솔루션

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51. n times. Each integration reduces the power of x by 1:

52. 1 time. The rst integration by parts gets rid of the ln x and turns the integrand into a sim-ple integral. See, for example, Problem 4.

53. (a) As the given problem, R x sin x2dx can be simplied by substituting x2 = u, we can solve the example using substitution method.
(b) As the given integral, R x2 sin x dx can not be simplied by substitution method and can be solved using method of integration by parts.
(c) As the integral, R x ln x dx can not be sim-plied by substitution and can be solved using the method of integration by parts.

<중 략>

6.6 Improper Integrals
1. (a) improper, function not dened at x = 0
(b) not improper, function continuous on entire interval
(c) not improper, function continuous on on entire interval

2. (a) improper, interval is innite
(b) improper, function not dened at x = 0
(c) improper, interval is innite

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