integral from 1 to 16 of (x-3)/(sqrt(x))

Lösung

\int_{1}^{16} \frac{x - 3}{x} d x

24

Schritte zur Lösung

\int_{1}^{16} \frac{x - 3}{x} d x

Multipliziere aus

\frac{x - 3}{x} : x - \frac{3}{x}

= \int_{1}^{16} x - \frac{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

= \int_{1}^{16} x d x - \int_{1}^{16} \frac{3}{x} d x

\int_{1}^{16} x d x = 42

\int_{1}^{16} \frac{3}{x} d x = 18

= 42 - 18

Vereinfache

= 24