integral from-4 to 6 of 12+x-1/2 x^2

Lösung

\int_{- 4}^{6} 12 + x - \frac{1}{2} x^{2} d x

\frac{250}{3}

Dezimale

83.33333 \dots

Schritte zur Lösung

\int_{- 4}^{6} 12 + x - \frac{1}{2} x^{2} 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

= \int_{- 4}^{6} 12 d x + \int_{- 4}^{6} x d x - \int_{- 4}^{6} \frac{1}{2} x^{2} d x

\int_{- 4}^{6} 12 d x = 120

\int_{- 4}^{6} x d x = 10

\int_{- 4}^{6} \frac{1}{2} x^{2} d x = \frac{140}{3}

= 120 + 10 - \frac{140}{3}

Vereinfache

120 + 10 - \frac{140}{3} : \frac{250}{3}

= \frac{250}{3}

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