What is the integral from 0 to 4 of 3e^{-x^2} ?

The integral from 0 to 4 of 3e^{-x^2} is 2.65868…

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integral from 0 to 4 of 3e^{-x^2}

\int_{0}^{4} 3 e^{- x^{2}} d x

2.65868 \dots

Solution steps

\int_{0}^{4} 3 e^{- x^{2}} d x

Take the constant out:

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

= 3 \cdot \int_{0}^{4} e^{- x^{2}} d x

Use the nonelementary integral:

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

= 3 [\frac{π}{2} erf (x)]_{0}^{4}

Compute the boundaries:

0.88622 \dots

= 3 \cdot 0.88622 \dots

Simplify

= 2.65868 \dots

f (x) = 9

\int cot (m) x csc^{2} (m) x d x

f (x) = 2 x^{3}, at x = - 1

\int sin (\frac{x}{5}) d x

a x^{3}, at x = - 5

What is the integral from 0 to 4 of 3e^{-x^2} ?
The integral from 0 to 4 of 3e^{-x^2} is 2.65868…