integral from 5 to x of 2/75 (x-5)

Lösung

\int_{5}^{x} \frac{2}{75} (x - 5) d x

\frac{1}{75} (x^{2} - 10 x + 25)

Schritte zur Lösung

\int_{5}^{x} \frac{2}{75} (x - 5) d x

Entferne die Konstante:

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

= \frac{2}{75} \cdot \int_{5}^{x} x - 5 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}{75} (\int_{5}^{x} x d x - \int_{5}^{x} 5 d x)

\int_{5}^{x} x d x = \frac{x ^{2} - 25}{2}

\int_{5}^{x} 5 d x = 5 x - 25

= \frac{2}{75} (\frac{x ^{2} - 25}{2} - (5 x - 25))

Vereinfache

\frac{2}{75} (\frac{x ^{2} - 25}{2} - (5 x - 25)) : \frac{1}{75} (x^{2} - 10 x + 25)

= \frac{1}{75} (x^{2} - 10 x + 25)

\int_{- π}^{π} sin (4 x) sin (4 x) d x

\int_{0}^{r} (b r^{2} + cr) d r

\int_{y - 2}^{2} (2) (- (y - x) + 2) d x

\int_{- 1}^{1} 1 3^{x} d x

\int_{- \infty}^{- 1} \frac{1}{x ^{5}} d x