integral from 1 to x of 2-x

Lösung

\int_{1}^{x} 2 - x d x

2 x - 2 - \frac{x ^{2} - 1}{2}

Schritte zur Lösung

\int_{1}^{x} 2 - 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

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

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

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

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