integral from 0 to 1 of sqrt(x)(x+1)

Lösung

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

\frac{16}{15}

Dezimale

1.06666 \dots

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

= \frac{2}{5} + \frac{2}{3}

Vereinfache

\frac{2}{5} + \frac{2}{3} : \frac{16}{15}

= \frac{16}{15}

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