What is the integral from 0 to 2 of 6e^{-x^2} ?

The integral from 0 to 2 of 6e^{-x^2} is 5.29248…

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integral from 0 to 2 of 6e^{-x^2}

\int_{0}^{2} 6 e^{- x^{2}} d x

5.29248 \dots

Solution steps

\int_{0}^{2} 6 e^{- x^{2}} d x

Take the constant out:

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

= 6 \cdot \int_{0}^{2} e^{- x^{2}} d x

Use the nonelementary integral:

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

= 6 [\frac{π}{2} erf (x)]_{0}^{2}

Compute the boundaries:

0.88208 \dots

= 6 \cdot 0.88208 \dots

Simplify

= 5.29248 \dots

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What is the integral from 0 to 2 of 6e^{-x^2} ?
The integral from 0 to 2 of 6e^{-x^2} is 5.29248…