What is the integral from 0 to 4 of 7e^{-x^2} ?

The integral from 0 to 4 of 7e^{-x^2} is 6.20358…

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integral from 0 to 4 of 7e^{-x^2}

\int_{0}^{4} 7 e^{- x^{2}} d x

6.20358 \dots

Solution steps

\int_{0}^{4} 7 e^{- x^{2}} d x

Take the constant out:

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

= 7 \cdot \int_{0}^{4} e^{- x^{2}} d x

Use the nonelementary integral:

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

= 7 [\frac{π}{2} erf (x)]_{0}^{4}

Compute the boundaries:

0.88622 \dots

= 7 \cdot 0.88622 \dots

Simplify

= 6.20358 \dots

F (x) = (7 x^{6} + 4 x^{3})^{4}

x \to 0 lim (\frac{1}{x - 4})

\int sin (x) sin (3 x) d x

\frac{d y}{d x}, y = x^{3 x}

f (x) = t

What is the integral from 0 to 4 of 7e^{-x^2} ?
The integral from 0 to 4 of 7e^{-x^2} is 6.20358…