integral from 0 to 1 of x(x+1)^{10}

Lösung

\int_{0}^{1} x (x + 1)^{10} d x

\frac{6827}{44}

Dezimale

155.15909 \dots

Schritte zur Lösung

\int_{0}^{1} x (x + 1)^{10} d x

Wende U-Substitution an

= \int_{1}^{2} (u - 1) u^{10} d u

Multipliziere aus

(u - 1) u^{10} : u^{11} - u^{10}

= \int_{1}^{2} u^{11} - u^{10} 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}^{2} u^{11} d u - \int_{1}^{2} u^{10} d u

\int_{1}^{2} u^{11} d u = \frac{1365}{4}

\int_{1}^{2} u^{10} d u = \frac{2047}{11}

= \frac{1365}{4} - \frac{2047}{11}

Vereinfache

\frac{1365}{4} - \frac{2047}{11} : \frac{6827}{44}

= \frac{6827}{44}

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