(a) Use your calculator to approximate ∫₀^b e^-x2 dx for b = 1, 5, 10, and 20.
(b) Based on your answers to part (a), does ∫₀^∞e^-x2 dx appear to be convergent or divergent? If convergent, what seems to be its approximate value?
(c) Explain why this integral should be convergent by comparing e^-x2 with e^-x for x > 1.