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

Lösung

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

\frac{2}{3}

Dezimale

0.66666 \dots

Schritte zur Lösung

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

Multipliziere aus

x^{2} (1 + 2 x^{3}) : x^{2} + 2 x^{5}

= \int_{0}^{1} x^{2} + 2 x^{5} d x

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}^{1} x^{2} d x + \int_{0}^{1} 2 x^{5} d x

\int_{0}^{1} x^{2} d x = \frac{1}{3}

\int_{0}^{1} 2 x^{5} d x = \frac{1}{3}

= \frac{1}{3} + \frac{1}{3}

Vereinfache

\frac{1}{3} + \frac{1}{3} : \frac{2}{3}

= \frac{2}{3}

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