Explain why each of the following integrals is improper. 9. (a) dx Is (x - 6)6 Since y= has a vertical asymptote at x=6, the integral is improper. (x – 6)6 Since y=- has a vertical asymptote at x=5, the integral is improper. (x – 6)6 Since the integral has an infinite interval of integration, the integral is improper. The integral is not improper. 8. (b) 7In(x) dx The integral is not improper. Since the integral has an infinite interval of integration, the integral is improper. Since y=In(x) has a vertical asymptote at x=1, the integral is improper. Since y=In(x) has a vertical asymptote at x=0, the integral is improper. T/4 (c) sec(x) dx Since y=sec(x) has a vertical asymptote at x=-4, the integral is improper. Since the integral has an infinite interval of integration, the integral is improper. The integral is not improper. Since y=sec(x) has a vertical asymptote at x=0, the integral is improper.

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