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

Lösung

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

\frac{e ^{8} - 1}{3 e ^{8}}

Dezimale

0.33322 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{- 8} - \frac{e ^{u}}{3} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 8}^{0} - \frac{e ^{u}}{3} d u

Entferne die Konstante:

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

= - (- \frac{1}{3} \cdot \int_{- 8}^{0} e^{u} d u)

Nutze das gemeinsame Integral :

\int e^{u} d u = e^{u}

= - (- \frac{1}{3} [e^{u}]_{- 8}^{0})

Vereinfache

= \frac{1}{3} [e^{u}]_{- 8}^{0}

Berechne die Grenzen:

1 - \frac{1}{e ^{8}}

= \frac{1}{3} (1 - \frac{1}{e ^{8}})

Vereinfache

= \frac{e ^{8} - 1}{3 e ^{8}}

\int_{0}^{12} x d x

\int_{0}^{2} \frac{1}{2 - x} d x

\int_{0}^{1} 2 - x d x

\int_{0}^{0.6} \frac{1}{1 + x} d x

\int_{- \frac{5 π}{6}}^{\frac{π}{3}} sin (x) d x