What is the integral from 4x to 4 of e^{-y^2} ?

The integral from 4x to 4 of e^{-y^2} is 0.88622…-0.88622…\erf(4x)

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integral from 4x to 4 of e^{-y^2}

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

0.88622 \dots - 0.88622 \dots erf (4 x)

Solution steps

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

Use the nonelementary integral:

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

= [\frac{π}{2} erf (y)]_{4 x}^{4}

Compute the boundaries:

0.88622 \dots - 0.88622 \dots erf (4 x)

= 0.88622 \dots - 0.88622 \dots erf (4 x)

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\int_{0}^{π} 1 - cos (θ) d θ

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What is the integral from 4x to 4 of e^{-y^2} ?
The integral from 4x to 4 of e^{-y^2} is 0.88622…-0.88622…\erf(4x)