integral from 0 to 3 of 7x(x-3)

Lösung

\int_{0}^{3} 7 x (x - 3) d x

- \frac{63}{2}

Dezimale

- 31.5

Schritte zur Lösung

\int_{0}^{3} 7 x (x - 3) d x

Entferne die Konstante:

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

= 7 \cdot \int_{0}^{3} x (x - 3) d x

Multipliziere aus

x (x - 3) : x^{2} - 3 x

= 7 \cdot \int_{0}^{3} x^{2} - 3 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

= 7 (\int_{0}^{3} x^{2} d x - \int_{0}^{3} 3 x d x)

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} 3 x d x = \frac{27}{2}

= 7 (9 - \frac{27}{2})

Vereinfache

7 (9 - \frac{27}{2}) : - \frac{63}{2}

= - \frac{63}{2}

\int_{6}^{7} t^{2} - 2 t - 24 d t

\int_{\frac{1}{2}}^{1} (x^{- 3} - 23) d x

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