integral of 1/2 (x-2)

Lösung

\int \frac{1}{2} (x - 2) d x

\frac{x ^{2}}{4} - x + C

Schritte zur Lösung

\int \frac{1}{2} (x - 2) d x

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int 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

= \frac{1}{2} (\int x d x - \int 2 d x)

\int x d x = \frac{x ^{2}}{2}

\int 2 d x = 2 x

= \frac{1}{2} (\frac{x ^{2}}{2} - 2 x)

Vereinfache

\frac{1}{2} (\frac{x ^{2}}{2} - 2 x) : \frac{x ^{2}}{4} - x

= \frac{x ^{2}}{4} - x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{4} - x + C

\int \frac{x ^{2}}{25 - 4 x ^{2}} d x

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