Decide if the improper integral ∫₀^∞ e^−2t dt converges ,and if so, to what value, by the following method.
(a) Use a computer or calculator to find ∫^b₀ e^−2t dt forb = 3, 5, 7, 10.What do you observe? Make a guess about the convergence of the improper integral.
(b) Find ∫^b₀ e^−2t dt using the Fundamental Theorem. Your answer will contain b.
(c) Take the limit b → ∞ of your answer to part (b). Does this limit confirm your guess from part (a)?