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

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

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

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

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

Solution steps

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

Compute the boundaries:

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

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

\int_{x}^{x^{2}} e^{x^{4}} d x

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\int_{0}^{\frac{1}{4}} arctan (4 x) d x

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