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
$\int_0^\infty e^{-x} dx$
= limA→∞ $\int_0^A e^{-x} dx$
= limA→∞ $\Big[-e^{-x} \Big]_0^A$ as the integral of emx is emx/m.
= limA→∞ $\Big(-e^{-A} + e^{0}\Big)$
= – limA→∞ $e^{-A}$ + 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. |
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