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

Lösung

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

\frac{4}{3}

Dezimale

1.33333 \dots

Schritte zur Lösung

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

\int_{0}^{4} x d x = \frac{16}{3}

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

= \frac{16}{3} - 4

Vereinfache

\frac{16}{3} - 4 : \frac{4}{3}

= \frac{4}{3}

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