What is the integral from 0 to infinity of e^{-9y^2} ?

The integral from 0 to infinity of e^{-9y^2} is (sqrt(pi))/6

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integral from 0 to infinity of e^{-9y^2}

\int_{0}^{\infty} e^{- 9 y^{2}} d y

\frac{π}{6}

Decimal

0.29540 \dots

Solution steps

\int_{0}^{\infty} e^{- 9 y^{2}} d y

Compute the indefinite integral:

\int e^{- 9 y^{2}} d y = \frac{π}{6} erf (9 y) + C

Compute the boundaries:

\int_{0}^{\infty} e^{- 9 y^{2}} d y = \frac{π}{6} - 0

= \frac{π}{6} - 0

Simplify

= \frac{π}{6}

What is the integral from 0 to infinity of e^{-9y^2} ?
The integral from 0 to infinity of e^{-9y^2} is (sqrt(pi))/6