What is the integral from 0 to x of 3e^{-t^2} ?

The integral from 0 to x of 3e^{-t^2} is (3sqrt(pi))/2 \erf(x)

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integral from 0 to x of 3e^{-t^2}

\int_{0}^{x} 3 e^{- t^{2}} d t

\frac{3 π}{2} erf (x)

Solution steps

\int_{0}^{x} 3 e^{- t^{2}} d t

Take the constant out:

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

= 3 \cdot \int_{0}^{x} e^{- t^{2}} d t

Use the nonelementary integral:

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

= 3 [\frac{π}{2} erf (t)]_{0}^{x}

Compute the boundaries:

\frac{π}{2} erf (x)

= 3 \cdot \frac{π}{2} erf (x)

Simplify

= \frac{3 π}{2} erf (x)

What is the integral from 0 to x of 3e^{-t^2} ?
The integral from 0 to x of 3e^{-t^2} is (3sqrt(pi))/2 \erf(x)