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

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

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

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

\frac{π}{2}

Decimal

0.88622 \dots

Solution steps

\int_{- \infty}^{\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_{- \infty}^{\infty} e^{- 4 x^{2}} d x = \frac{π}{4} - (- \frac{π}{4})

= \frac{π}{4} - (- \frac{π}{4})

Simplify

= \frac{π}{2}

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