What is the integral from 0 to sin(x) of e^{-t^2} ?

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

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integral from 0 to sin(x) of e^{-t^2}

\int_{0}^{s i n (x)} e^{- t^{2}} d t

\frac{π}{2} erf (sin (x))

Solution steps

\int_{0}^{s i n (x)} e^{- t^{2}} d t

Use the nonelementary integral:

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

= [\frac{π}{2} erf (t)]_{0}^{s i n (x)}

Compute the boundaries:

\frac{π}{2} erf (sin (x))

= \frac{π}{2} erf (sin (x))

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