integral from 0 to 4 of (x+1)-x/2

Lösung

\int_{0}^{4} (x + 1) - \frac{x}{2} d x

8

Schritte zur Lösung

\int_{0}^{4} x + 1 - \frac{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}^{4} x d x + \int_{0}^{4} 1 d x - \int_{0}^{4} \frac{x}{2} d x

\int_{0}^{4} x d x = 8

\int_{0}^{4} 1 d x = 4

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

= 8 + 4 - 4

Vereinfache

= 8

\int_{0}^{x} t (t - sin (t)) d t

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