Integral of e^(-x) from 0 to Infinity

The integral of e^(-x) from 0 to infinity is equal to 1. Here we will learn how to integrate e^-x (e to the power -x) from 0 to ∞.

Answer: The integral of e^-x from 0 to infinity is equal to 1. That is, $\int_0^\infty e^{-x} dx =1$.

Explanation:

The integration of e^-x from 0 to infinity is given by

$\int_0^\infty e^{-x} dx$

= lim_A→∞ $\int_0^A e^{-x} dx$

= lim_A→∞ $\Big[-e^{-x} \Big]_0^A$ as the integral of e^mx is e^mx/m.

= lim_A→∞ $\Big(-e^{-A} + e^{0}\Big)$

= – lim_A→∞ $e^{-A}$ + 1

= – 0 + 1

= 1.

So the integral of e^-x from 0 to infinity is equal to 1, that is, ∫₀^∞ e^-x dx =1.

Remark: The integral of e^-ax from 0 to infinity is equal to 1/a, That is
∫₀^∞ e^-ax dx = 1/a.

Read Also:

Integral of log(sinx) from 0 to pi/2

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