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Beliebt Rechnen >

integral from 0 to 12 of xsqrt(12-x)

Lösung

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

Lösung

- \frac{576 3}{5} + 1923

+1

Dezimale

133.02150 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{12}^{0} - (- u + 12) u d u

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

= - \int_{0}^{12} - (- u + 12) u d u

Entferne die Konstante:

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

= - (- \int_{0}^{12} (- u + 12) u d u)

Multipliziere aus

(- u + 12) u : - u^{\frac{3}{2}} + 12 u

= - (- \int_{0}^{12} - u^{\frac{3}{2}} + 12 u d u)

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - (- (- \int_{0}^{12} u^{\frac{3}{2}} d u + \int_{0}^{12} 12 u d u))

\int_{0}^{12} u^{\frac{3}{2}} d u = \frac{576 3}{5}

\int_{0}^{12} 12 u d u = 1923

= - (- (- \frac{576 3}{5} + 1923))

Vereinfache

= - \frac{576 3}{5} + 1923

Graph

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