integral from 4 to 16 of (x-1)sqrt(x)

Lösung

\int_{4}^{16} (x - 1) x d x

\frac{5392}{15}

Dezimale

359.46666 \dots

Schritte zur Lösung

\int_{4}^{16} (x - 1) x d x

Multipliziere aus

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

= \int_{4}^{16} 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_{4}^{16} x^{\frac{3}{2}} d x - \int_{4}^{16} x d x

\int_{4}^{16} x^{\frac{3}{2}} d x = \frac{1984}{5}

\int_{4}^{16} x d x = \frac{112}{3}

= \frac{1984}{5} - \frac{112}{3}

Vereinfache

\frac{1984}{5} - \frac{112}{3} : \frac{5392}{15}

= \frac{5392}{15}

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

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