integral from 0 to 1 of x^7e^{-x^4}

Lösung

\int_{0}^{1} x^{7} e^{- x^{4}} d x

- \frac{- e + 2}{4 e}

Dezimale

0.06606 \dots

Schritte zur Lösung

\int_{0}^{1} x^{7} e^{- x^{4}} d x

Wende U-Substitution an

= \int_{0}^{- 1} \frac{e ^{u} u}{4} d u

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

= - \int_{- 1}^{0} \frac{e ^{u} u}{4} d u

Entferne die Konstante:

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

= - \frac{1}{4} \cdot \int_{- 1}^{0} e^{u} u d u

Wende die partielle Integration an

= - \frac{1}{4} [e^{u} u - \int e^{u} d u]_{- 1}^{0}

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

= - \frac{1}{4} [e^{u} u - e^{u}]_{- 1}^{0}

Berechne die Grenzen:

- 1 + \frac{2}{e}

= - \frac{1}{4} (- 1 + \frac{2}{e})

Vereinfache

= - \frac{- e + 2}{4 e}

\int_{- 1}^{2} 4 x - 6 x^{2} d x

\int_{0}^{a} 9 x a^{2} - x^{2} d x

\int_{- 1}^{1} x^{2} ∣ x ∣ d x

\int_{- e^{6}}^{- e^{3}} \frac{1}{x} d x

\int_{2}^{3} (x^{3}) d x