integral from 1 to 4 of (x^2-4x+5)

Lösung

\int_{1}^{4} (x^{2} - 4 x + 5) d x

6

Schritte zur Lösung

\int_{1}^{4} x^{2} - 4 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

= \int_{1}^{4} x^{2} d x - \int_{1}^{4} 4 x d x + \int_{1}^{4} 5 d x

\int_{1}^{4} x^{2} d x = 21

\int_{1}^{4} 4 x d x = 30

\int_{1}^{4} 5 d x = 15

= 21 - 30 + 15

Vereinfache

= 6