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Beliebt Rechnen >

integral from-2 to 6 of x^2\sqrt[3]{x+2}

Lösung

\int_{- 2}^{6} x^{2} 3 x + 2 d x

Lösung

\frac{4752}{35}

+1

Dezimale

135.77142 \dots

Schritte zur Lösung

\int_{- 2}^{6} x^{2} 3 x + 2 d x

Wende U-Substitution an

= \int_{0}^{8} (u - 2)^{2} 3 u d u

Multipliziere aus

(u - 2)^{2} 3 u : u^{\frac{7}{3}} - 4 u^{\frac{4}{3}} + 4 3 u

= \int_{0}^{8} u^{\frac{7}{3}} - 4 u^{\frac{4}{3}} + 4 3 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}^{8} u^{\frac{7}{3}} d u - \int_{0}^{8} 4 u^{\frac{4}{3}} d u + \int_{0}^{8} 4 3 u d u

\int_{0}^{8} u^{\frac{7}{3}} d u = \frac{1536}{5}

\int_{0}^{8} 4 u^{\frac{4}{3}} d u = \frac{1536}{7}

\int_{0}^{8} 4 3 u d u = 48

= \frac{1536}{5} - \frac{1536}{7} + 48

Vereinfache

\frac{1536}{5} - \frac{1536}{7} + 48 : \frac{4752}{35}

= \frac{4752}{35}

Graph

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