integral from 0 to 2 of (6-t)sqrt(t)

Lösung

\int_{0}^{2} (6 - t) t d t

82 - \frac{8 2}{5}

Dezimale

9.05096 \dots

Schritte zur Lösung

\int_{0}^{2} (6 - t) t d t

Multipliziere aus

(6 - t) t : 6 t - t^{\frac{3}{2}}

= \int_{0}^{2} 6 t - t^{\frac{3}{2}} d t

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}^{2} 6 t d t - \int_{0}^{2} t^{\frac{3}{2}} d t

\int_{0}^{2} 6 t d t = 82

\int_{0}^{2} t^{\frac{3}{2}} d t = \frac{8 2}{5}

= 82 - \frac{8 2}{5}

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