integral from 0 to 3 of 10t(75-t^2)

Lösung

\int_{0}^{3} 10 t (75 - t^{2}) d t

\frac{6345}{2}

Dezimale

3172.5

Schritte zur Lösung

\int_{0}^{3} 10 t (75 - t^{2}) d t

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \int_{0}^{3} t (75 - t^{2}) d t

Multipliziere aus

t (75 - t^{2}) : 75 t - t^{3}

= 10 \cdot \int_{0}^{3} 75 t - t^{3} 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

= 10 (\int_{0}^{3} 75 t d t - \int_{0}^{3} t^{3} d t)

\int_{0}^{3} 75 t d t = \frac{675}{2}

\int_{0}^{3} t^{3} d t = \frac{81}{4}

= 10 (\frac{675}{2} - \frac{81}{4})

Vereinfache

10 (\frac{675}{2} - \frac{81}{4}) : \frac{6345}{2}

= \frac{6345}{2}

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