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

Lösung

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

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

Dezimale

- 0.72134 \dots

Schritte zur Lösung

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

Berechne das unbestimmte Integral:

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

Berechne die Grenzen:

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

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

Vereinfache

= - \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_{1}^{3 x} ln (x) d x