integral from 1 to 3 of (3x-y)/9

Lösung

\int_{1}^{3} \frac{3 x - y}{9} d x

\frac{1}{9} (- 2 y + 12)

Schritte zur Lösung

\int_{1}^{3} \frac{3 x - y}{9} d x

Entferne die Konstante:

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

= \frac{1}{9} \cdot \int_{1}^{3} - y + 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

= \frac{1}{9} (- \int_{1}^{3} y d x + \int_{1}^{3} 3 x d x)

\int_{1}^{3} y d x = 2 y

\int_{1}^{3} 3 x d x = 12

= \frac{1}{9} (- 2 y + 12)

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