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

Lösung

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

\frac{3}{40}

Dezimale

0.075

Schritte zur Lösung

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

Multipliziere aus

x^{3} (x - \frac{1}{2}) : x^{4} - \frac{x ^{3}}{2}

= \int_{0}^{1} x^{4} - \frac{x ^{3}}{2} 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^{4} d x - \int_{0}^{1} \frac{x ^{3}}{2} d x

\int_{0}^{1} x^{4} d x = \frac{1}{5}

\int_{0}^{1} \frac{x ^{3}}{2} d x = \frac{1}{8}

= \frac{1}{5} - \frac{1}{8}

Vereinfache

\frac{1}{5} - \frac{1}{8} : \frac{3}{40}

= \frac{3}{40}

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