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

The integral from 0 to y of e^{-x^2} is (sqrt(pi))/2 \erf(y)

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

\int_{0}^{y} e^{- x^{2}} d x

\frac{π}{2} erf (y)

Solution steps

\int_{0}^{y} e^{- x^{2}} d x

Use the nonelementary integral:

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

= [\frac{π}{2} erf (x)]_{0}^{y}

Compute the boundaries:

\frac{π}{2} erf (y)

= \frac{π}{2} erf (y)

\int_{- 1}^{2} x^{2} - 1 d x

\int_{0}^{4} 5 d x

\int_{0}^{π} 5 e^{x} + 3 sin (x) d x

\int_{0}^{\frac{π}{2}} 3 sin (x) d x

\int_{5}^{7} 1 d x

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