What is the integral from 0 to infinity of e^{-3x^2} ?

The integral from 0 to infinity of e^{-3x^2} is (sqrt(pi))/(2sqrt(3))

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integral from 0 to infinity of e^{-3x^2}

\int_{0}^{\infty} e^{- 3 x^{2}} d x

\frac{π}{2 3}

Decimal

0.51166 \dots

Solution steps

\int_{0}^{\infty} e^{- 3 x^{2}} d x

Compute the indefinite integral:

\int e^{- 3 x^{2}} d x = \frac{π}{2 3} erf (3 x) + C

Compute the boundaries:

\int_{0}^{\infty} e^{- 3 x^{2}} d x = \frac{π}{2 3} - 0

= \frac{π}{2 3} - 0

Simplify

= \frac{π}{2 3}

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What is the integral from 0 to infinity of e^{-3x^2} ?
The integral from 0 to infinity of e^{-3x^2} is (sqrt(pi))/(2sqrt(3))