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Beliebt Rechnen >

integral from-3 to 0 of xsqrt(1-x)

Lösung

\int_{- 3}^{0} x 1 - x d x

Lösung

- \frac{116}{15}

+1

Dezimale

- 7.73333 \dots

Schritte zur Lösung

\int_{- 3}^{0} x 1 - x d x

Wende U-Substitution an

= \int_{4}^{1} - (- u + 1) u d u

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

= - \int_{1}^{4} - (- u + 1) u d u

Entferne die Konstante:

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

= - (- \int_{1}^{4} (- u + 1) u d u)

Multipliziere aus

(- u + 1) u : - u^{\frac{3}{2}} + u

= - (- \int_{1}^{4} - u^{\frac{3}{2}} + 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_{1}^{4} u^{\frac{3}{2}} d u + \int_{1}^{4} u d u))

\int_{1}^{4} u^{\frac{3}{2}} d u = \frac{62}{5}

\int_{1}^{4} u d u = \frac{14}{3}

= - (- (- \frac{62}{5} + \frac{14}{3}))

Vereinfache

- (- (- \frac{62}{5} + \frac{14}{3})) : - \frac{116}{15}

= - \frac{116}{15}

Graph

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\int 6 x e^{x} d x

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\frac{d}{d x} (\frac{2}{1 - 6 x})

integral of 1/9

\int \frac{1}{9}