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

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

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

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

\frac{π}{2} erf (tan (x))

Solution steps

\int_{0}^{t a 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}^{t a n (x)}

Compute the boundaries:

\frac{π}{2} erf (tan (x))

= \frac{π}{2} erf (tan (x))

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\int_{3}^{5} 2 x d x

\int_{π}^{2 π} x sin (x) d x

\int_{0.5}^{0.75} 4 x^{3} d x

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

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