integral from 2 to 4 of (2(1+x))/(27)

Lösung

\int_{2}^{4} \frac{2 ( 1 + x )}{27} d x

\frac{16}{27}

Dezimale

0.59259 \dots

Schritte zur Lösung

\int_{2}^{4} \frac{2 ( 1 + x )}{27} d x

Entferne die Konstante:

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

= \frac{2}{27} \cdot \int_{2}^{4} 1 + 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

= \frac{2}{27} (\int_{2}^{4} 1 d x + \int_{2}^{4} x d x)

\int_{2}^{4} 1 d x = 2

\int_{2}^{4} x d x = 6

= \frac{2}{27} (2 + 6)

Vereinfache

\frac{2}{27} (2 + 6) : \frac{16}{27}

= \frac{16}{27}

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