17. Determine if the following integrals converge or diverge. If the integral converges, determine its value.
Show your work carefully, writing the improper integral as a limit of an intermediate ordinary integral.
You must evaluate the intermediate integral, and you must use proper limit notation, to obtain credit
here.
(a) $\int_0^\infty (1 + 2x)e^{-x} dx$
(b) $\int_{-\infty}^0 (1 + 2x)e^{-x} dx$
(c) $\int_{-\infty}^1 \sqrt{6 - y} dy$
(d) $\int_2^4 \frac{1}{x^2 + x - 6} dx$
(e) $\int_3^\infty \frac{e^{-3x}}{9 + e^{-3x}} dx$
(f) $\int_1^3 \frac{1}{\sqrt{x - 1}} dx$
