What is the integral from 0 to infinity of e^{-t^2} ?

The integral from 0 to infinity of e^{-t^2} is (sqrt(pi))/2

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integral from 0 to infinity of e^{-t^2}

\int_{0}^{\infty} e^{- t^{2}} d t

\frac{π}{2}

Solution steps

\int_{0}^{\infty} e^{- t^{2}} d t

Compute the indefinite integral:

\int e^{- t^{2}} d t = \frac{π}{2} erf (t) + C

Compute the boundaries:

\int_{0}^{\infty} e^{- t^{2}} d t = \frac{π}{2} - 0

= \frac{π}{2} - 0

Simplify

= \frac{π}{2}

f (x) = - 352

3 e^{x} + 4

x \to 1 - lim (\frac{x - 9}{∣ x - 9 ∣})

\int 2^{3 - 2 x} d x

- 2 x^{2} - 1

What is the integral from 0 to infinity of e^{-t^2} ?
The integral from 0 to infinity of e^{-t^2} is (sqrt(pi))/2