Question

Calculate the area under the curve y = e^-x above the x-axis, on the interval [1, infinity).

Answer 1

That's equivalent to finding the integral : \[\int\limits_{1}^{\infty} e ^{-x}dx\]

Answer 2

$$\int_1^a e^{-x} dx=\left[-e^{-x}\right]_1^a=-e^{-a}+e^{-1}$$so$$\lim_{a\to\infty}\int_1^a e^{-x} dx=e^{-1}=\frac1e$$