integral from 0 to 8 of sqrt(8x+36)

Lösung

\int_{0}^{8} 8 x + 36 d x

\frac{196}{3}

Dezimale

65.33333 \dots

Schritte zur Lösung

\int_{0}^{8} 8 x + 36 d x

Wende U-Substitution an

= \int_{36}^{100} \frac{u}{8} d u

Entferne die Konstante:

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

= \frac{1}{8} \cdot \int_{36}^{100} u d u

Wende die Potenzregel an

= \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{36}^{100}

Berechne die Grenzen:

\frac{1568}{3}

= \frac{1}{8} \cdot \frac{1568}{3}

Vereinfache

= \frac{196}{3}

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