integral from 0 to t^{10 of}sqrt(u^7)

Lösung

\int_{0}^{t^{10}} u^{7} d u

\frac{2 t ^{45}}{9}

Schritte zur Lösung

\int_{0}^{t^{10}} u^{7} d u

u^{7} = u^{\frac{7}{2}},

angenommen

u \geq 0

= \int_{0}^{t^{10}} u^{\frac{7}{2}} d u

Wende die Potenzregel an

= [\frac{2}{9} u^{\frac{9}{2}}]_{0}^{t^{10}}

Berechne die Grenzen:

\frac{2}{9} t^{45}

= \frac{2}{9} t^{45}

Vereinfache

= \frac{2 t ^{45}}{9}