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

The integral from-2 to 2 of e^{-x^2} is 1.76416…

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

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

1.76416 \dots

Solution steps

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

Use the nonelementary integral:

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

= [\frac{π}{2} erf (x)]_{- 2}^{2}

Compute the boundaries:

1.76416 \dots

= 1.76416 \dots

y = 2 x - 2 x^{2}

x \to 2 lim (\frac{1}{2} x^{2} - 4 x)

2 e^{2 t}

x = - 2, x = 3, y = 2 x^{2} + 2, y = 0

2 x^{2} + x - 1, at x = - 1

What is the integral from-2 to 2 of e^{-x^2} ?
The integral from-2 to 2 of e^{-x^2} is 1.76416…