integral from 0 to k of sqrt(x+3)

Lösung

\int_{0}^{k} x + 3 d x

\frac{2 ( k + 3 ) ^{\frac{3}{2}}}{3} - 23

Schritte zur Lösung

\int_{0}^{k} x + 3 d x

Wende U-Substitution an

= \int_{3}^{k + 3} u d u

Wende die Potenzregel an

= [\frac{2}{3} u^{\frac{3}{2}}]_{3}^{k + 3}

Berechne die Grenzen:

\frac{2}{3} (k + 3)^{\frac{3}{2}} - 23

= \frac{2}{3} (k + 3)^{\frac{3}{2}} - 23

Vereinfache

= \frac{2 ( k + 3 ) ^{\frac{3}{2}}}{3} - 23

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