What is the integral from 0 to 4 of 5e^{-x^2} ?

The integral from 0 to 4 of 5e^{-x^2} is 4.43113…

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integral from 0 to 4 of 5e^{-x^2}

\int_{0}^{4} 5 e^{- x^{2}} d x

4.43113 \dots

Solution steps

\int_{0}^{4} 5 e^{- x^{2}} d x

Take the constant out:

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

= 5 \cdot \int_{0}^{4} e^{- x^{2}} d x

Use the nonelementary integral:

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

= 5 [\frac{π}{2} erf (x)]_{0}^{4}

Compute the boundaries:

0.88622 \dots

= 5 \cdot 0.88622 \dots

Simplify

= 4.43113 \dots

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What is the integral from 0 to 4 of 5e^{-x^2} ?
The integral from 0 to 4 of 5e^{-x^2} is 4.43113…