integral from 0 to 8 of sqrt(1+81/4 x)

Lösung

\int_{0}^{8} 1 + \frac{81}{4} x d x

\frac{4 ( 326 163 - 2 )}{243}

Dezimale

68.47883 \dots

Schritte zur Lösung

\int_{0}^{8} 1 + \frac{81}{4} x d x

Wende U-Substitution an

= \int_{1}^{163} \frac{4 u}{81} d u

Entferne die Konstante:

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

= \frac{4}{81} \cdot \int_{1}^{163} u d u

Wende die Potenzregel an

= \frac{4}{81} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{163}

Berechne die Grenzen:

\frac{326 163}{3} - \frac{2}{3}

= \frac{4}{81} (\frac{326 163}{3} - \frac{2}{3})

Vereinfache

= \frac{4 ( 326 163 - 2 )}{243}

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