integral from 0 to 1 of (x+y)/z

Lösung

\int_{0}^{1} \frac{x + y}{z} d x

\frac{1}{z} (y + \frac{1}{2})

Schritte zur Lösung

\int_{0}^{1} \frac{x + y}{z} d x

Entferne die Konstante:

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

= \frac{1}{z} \cdot \int_{0}^{1} y + 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{1}{z} (\int_{0}^{1} y d x + \int_{0}^{1} x d x)

\int_{0}^{1} y d x = y

\int_{0}^{1} x d x = \frac{1}{2}

= \frac{1}{z} (y + \frac{1}{2})

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