integral from-4 to 4 of (2-sqrt(x))

Lösung

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

\frac{32}{3} - i \frac{16}{3}

Schritte zur Lösung

\int_{- 4}^{4} 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_{- 4}^{4} 2 d x - \int_{- 4}^{4} x d x

\int_{- 4}^{4} 2 d x = 16

\int_{- 4}^{4} x d x = \frac{16}{3} + i \frac{16}{3}

= 16 - (\frac{16}{3} + i \frac{16}{3})

Vereinfache

16 - (\frac{16}{3} + i \frac{16}{3}) : \frac{32}{3} - i \frac{16}{3}

= \frac{32}{3} - i \frac{16}{3}