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. |

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Integral of square root of tanx