Explain why each of the following integrals is improper. (a) dx (x - 9)3 O since y=- - has a vertical asymptote at x=8, the integral is improper. (x - 9)3 O since y=- (x – 9)3 O Since the integral has an infinite interval of integration, the integral is improper. O The integral is not improper. - has a vertical asymptote at x=9, the integral is improper. (b) 10ln(x) dx O Since y=In(x) has a vertical asymptote at x=1, the integral is improper. O Since the integral has an infinite interval of integration, the integral is improper. O The integral is not improper. O Since y=In(x) has a vertical asymptote at x=0, the integral is improper. (c) 1 dx (x+4)9 Since the integral has an infinite interval of integration, the integral is improper. Since y=1 (x+4)9 - has a vertical asymptote at x=-4, the integral is improper. O The integral is not improper. O Since y=, (x+4)9 1 - has a vertical asymptote at x=0, the integral is improper. m/2 (d) | 3sec(x) dx Since y=3sec(x) has a vertical asymptote at x=, the integral is improper. Since the integral has an infinite interval of integration, the integral is improper. Since y=3sec(x) has a vertical asymptote at x=, the integral is improper. O The integral is not improper.

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