integral from 0 to 4 of (14-t)sqrt(t)

Lösung

\int_{0}^{4} (14 - t) t d t

\frac{928}{15}

Dezimale

61.86666 \dots

Schritte zur Lösung

\int_{0}^{4} (14 - t) t d t

Multipliziere aus

(14 - t) t : 14 t - t^{\frac{3}{2}}

= \int_{0}^{4} 14 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}^{4} 14 t d t - \int_{0}^{4} t^{\frac{3}{2}} d t

\int_{0}^{4} 14 t d t = \frac{224}{3}

\int_{0}^{4} t^{\frac{3}{2}} d t = \frac{64}{5}

= \frac{224}{3} - \frac{64}{5}

Vereinfache

\frac{224}{3} - \frac{64}{5} : \frac{928}{15}

= \frac{928}{15}

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