integral from 0 to s of 40s^{1/2}

Lösung

\int_{0}^{s} 40 s^{\frac{1}{2}} d s

\frac{80 s ^{\frac{3}{2}}}{3}

Schritte zur Lösung

\int_{0}^{s} 40 s^{\frac{1}{2}} d s

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 40 \cdot \int_{0}^{s} s^{\frac{1}{2}} d s

Wende die Potenzregel an

= 40 [\frac{2}{3} s^{\frac{3}{2}}]_{0}^{s}

Berechne die Grenzen:

\frac{2}{3} s^{\frac{3}{2}}

= 40 \cdot \frac{2}{3} s^{\frac{3}{2}}

Vereinfache

= \frac{80 s ^{\frac{3}{2}}}{3}

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