integral from 0 to 7 of 2t^2-20t+48

Lösung

\int_{0}^{7} 2 t^{2} - 20 t + 48 d t

\frac{224}{3}

Dezimale

74.66666 \dots

Schritte zur Lösung

\int_{0}^{7} 2 t^{2} - 20 t + 48 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}^{7} 2 t^{2} d t - \int_{0}^{7} 20 t d t + \int_{0}^{7} 48 d t

\int_{0}^{7} 2 t^{2} d t = \frac{686}{3}

\int_{0}^{7} 20 t d t = 490

\int_{0}^{7} 48 d t = 336

= \frac{686}{3} - 490 + 336

Vereinfache

\frac{686}{3} - 490 + 336 : \frac{224}{3}

= \frac{224}{3}

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