integral from 0 to 4 of sqrt(x)(4-x)

Lösung

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

\frac{128}{15}

Dezimale

8.53333 \dots

Schritte zur Lösung

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

Multipliziere aus

x (4 - x) : 4 x - x^{\frac{3}{2}}

= \int_{0}^{4} 4 x - x^{\frac{3}{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} 4 x d x - \int_{0}^{4} x^{\frac{3}{2}} d x

\int_{0}^{4} 4 x d x = \frac{64}{3}

\int_{0}^{4} x^{\frac{3}{2}} d x = \frac{64}{5}

= \frac{64}{3} - \frac{64}{5}

Vereinfache

\frac{64}{3} - \frac{64}{5} : \frac{128}{15}

= \frac{128}{15}