What is the integral from 1 to cos(x) of e^{-t^2} ?

The integral from 1 to cos(x) of e^{-t^2} is 0.88622…\erf(cos(x))-0.74682…

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integral from 1 to cos(x) of e^{-t^2}

\int_{1}^{c o s (x)} e^{- t^{2}} d t

0.88622 \dots erf (cos (x)) - 0.74682 \dots

Solution steps

\int_{1}^{c o s (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)]_{1}^{c o s (x)}

Compute the boundaries:

0.88622 \dots erf (cos (x)) - 0.74682 \dots

= 0.88622 \dots erf (cos (x)) - 0.74682 \dots

What is the integral from 1 to cos(x) of e^{-t^2} ?
The integral from 1 to cos(x) of e^{-t^2} is 0.88622…\erf(cos(x))-0.74682…