What is the integral from-infinity to 0 of x2^{-x^2} ?

The integral from-infinity to 0 of x2^{-x^2} is -1/(2ln(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-infinity to 0 of x2^{-x^2}

\int_{- \infty}^{0} x 2^{- x^{2}} d x

- \frac{1}{2 ln ( 2 )}

Decimal Notation

- 0.72134 \dots

Solution steps

\int_{- \infty}^{0} x \cdot 2^{- x^{2}} d x

Compute the indefinite integral:

\int x \cdot 2^{- x^{2}} d x = - \frac{2 ^{- x^{2} - 1}}{ln ( 2 )} + C

Compute the boundaries:

\int_{- \infty}^{0} x \cdot 2^{- x^{2}} d x = - \frac{1}{2 ln ( 2 )} - 0

= - \frac{1}{2 ln ( 2 )} - 0

Simplify

= - \frac{1}{2 ln ( 2 )}

\int_{- 1}^{3} x e^{(2 - x)} d x

\int_{1}^{4} 3 x - 3 d x

\int_{- \infty}^{- 1} \frac{e ^{x}}{x} d x

\int_{0}^{6} \frac{x}{18} d x

\int_{- 0.5}^{0.5} 1 - x^{2} d x

What is the integral from-infinity to 0 of x2^{-x^2} ?
The integral from-infinity to 0 of x2^{-x^2} is -1/(2ln(2))