integral from 0 to 4 of (5-x)sqrt(x)

Lösung

\int_{0}^{4} (5 - x) x d x

\frac{208}{15}

Dezimale

13.86666 \dots

Schritte zur Lösung

\int_{0}^{4} (5 - x) x d x

Multipliziere aus

(5 - x) x : 5 x - x^{\frac{3}{2}}

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

\int_{0}^{4} 5 x d x = \frac{80}{3}

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

= \frac{80}{3} - \frac{64}{5}

Vereinfache

\frac{80}{3} - \frac{64}{5} : \frac{208}{15}

= \frac{208}{15}

roo t s x e^{y}

\int \frac{1}{x ^{2} + 4 x - 5} d x

t^{2} y^{^{'}} + 2 t y = y^{3}

x \to 0 lim (x + 2)

n or ma l y = x^{2} - 4 x, (7, 21)