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

Lösung

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

\frac{5}{12}

Dezimale

0.41666 \dots

Schritte zur Lösung

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

Multipliziere aus

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

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

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

\int_{0}^{1} \frac{x ^{2}}{2} d x = \frac{1}{6}

= \frac{1}{4} + \frac{1}{6}

Vereinfache

\frac{1}{4} + \frac{1}{6} : \frac{5}{12}

= \frac{5}{12}

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\int_{x}^{0} t^{2} + 4 d t