What is the integral from 0 to infinity of e^{-4x^2} ?

The integral from 0 to infinity of e^{-4x^2} is (sqrt(pi))/4

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integral from 0 to infinity of e^{-4x^2}

\int_{0}^{\infty} e^{- 4 x^{2}} d x

\frac{π}{4}

Decimal

0.44311 \dots

Solution steps

\int_{0}^{\infty} e^{- 4 x^{2}} d x

Compute the indefinite integral:

\int e^{- 4 x^{2}} d x = \frac{π}{4} erf (4 x) + C

Compute the boundaries:

\int_{0}^{\infty} e^{- 4 x^{2}} d x = \frac{π}{4} - 0

= \frac{π}{4} - 0

Simplify

= \frac{π}{4}

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What is the integral from 0 to infinity of e^{-4x^2} ?
The integral from 0 to infinity of e^{-4x^2} is (sqrt(pi))/4