integral from 0 to 3 of (2x-x^2)^3(1-x)

Lösung

\int_{0}^{3} (2 x - x^{2})^{3} (1 - x) d x

\frac{81}{8}

Dezimale

10.125

Schritte zur Lösung

\int_{0}^{3} (2 x - x^{2})^{3} (1 - x) d x

Wende U-Substitution an

= \int_{0}^{- 3} \frac{u ^{3}}{2} d u

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

= - \int_{- 3}^{0} \frac{u ^{3}}{2} d u

Entferne die Konstante:

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

= - \frac{1}{2} \cdot \int_{- 3}^{0} u^{3} d u

Wende die Potenzregel an

= - \frac{1}{2} [\frac{u ^{4}}{4}]_{- 3}^{0}

Berechne die Grenzen:

- \frac{81}{4}

= - \frac{1}{2} (- \frac{81}{4})

Vereinfache

= \frac{81}{8}

\frac{\partial}{\partial x} (z^{2} cos (y x))

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