integral from 1 to 12 of (1-x)(x-12)

Lösung

\int_{1}^{12} (1 - x) (x - 12) d x

\frac{1331}{6}

Dezimale

221.83333 \dots

Schritte zur Lösung

\int_{1}^{12} (1 - x) (x - 12) d x

Multipliziere aus

(1 - x) (x - 12) : 13 x - x^{2} - 12

= \int_{1}^{12} 13 x - x^{2} - 12 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_{1}^{12} 13 x d x - \int_{1}^{12} x^{2} d x - \int_{1}^{12} 12 d x

\int_{1}^{12} 13 x d x = \frac{1859}{2}

\int_{1}^{12} x^{2} d x = \frac{1727}{3}

\int_{1}^{12} 12 d x = 132

= \frac{1859}{2} - \frac{1727}{3} - 132

Vereinfache

\frac{1859}{2} - \frac{1727}{3} - 132 : \frac{1331}{6}

= \frac{1331}{6}

\int_{2}^{3} 32 x - 63 d x

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\int_{- 1}^{2} π (\frac{x ^{3}}{4} + 1)^{2} d x

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