What is the integral from 0 to 0.3 of 4e^{-x^2} ?

The integral from 0 to 0.3 of 4e^{-x^2} is 1.16495…

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integral from 0 to 0.3 of 4e^{-x^2}

\int_{0}^{0.3} 4 e^{- x^{2}} d x

1.16495 \dots

Solution steps

\int_{0}^{0.3} 4 e^{- x^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int_{0}^{0.3} e^{- x^{2}} d x

Use the nonelementary integral:

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

= 4 [\frac{π}{2} erf (x)]_{0}^{0.3}

Simplify

= 4 [0.88622 \dots erf (x)]_{0}^{0.3}

Compute the boundaries:

0.29123 \dots

= 4 \cdot 0.29123 \dots

Simplify

= 1.16495 \dots

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What is the integral from 0 to 0.3 of 4e^{-x^2} ?
The integral from 0 to 0.3 of 4e^{-x^2} is 1.16495…