integral from 0 to 3 of sqrt(1+81/64 x)

Lösung

\int_{0}^{3} 1 + \frac{81}{64} x d x

\frac{307 307 - 512}{972}

Dezimale

5.00727 \dots

Schritte zur Lösung

\int_{0}^{3} 1 + \frac{81}{64} x d x

Wende U-Substitution an

= \int_{1}^{\frac{307}{64}} \frac{64 u}{81} d u

Entferne die Konstante:

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

= \frac{64}{81} \cdot \int_{1}^{\frac{307}{64}} u d u

Wende die Potenzregel an

= \frac{64}{81} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{\frac{307}{64}}

Berechne die Grenzen:

\frac{307 307}{768} - \frac{2}{3}

= \frac{64}{81} (\frac{307 307}{768} - \frac{2}{3})

Vereinfache

= \frac{307 307 - 512}{972}

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