integral from 0 to 2 of |x-2|

Lösung

\int_{0}^{2} ∣ x - 2 ∣ d x

2

Schritte zur Lösung

\int_{0}^{2} ∣ x - 2 ∣ d x

Entferne die Extremwerte

= \int_{0}^{2} - 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

= - \int_{0}^{2} x d x + \int_{0}^{2} 2 d x

\int_{0}^{2} x d x = 2

\int_{0}^{2} 2 d x = 4

= - 2 + 4

Vereinfache

= 2

\int_{0}^{6} 6 - x d x

\int_{c}^{6} \frac{1}{4} d x

\int_{0}^{7} 49 - t^{2} d t

\int_{0}^{1} \frac{1}{3 x + 1} d x

\int_{- 2}^{2} (4 x - x^{3}) d x