integral from 0 to 4 of 8/(sqrt(7x+6))

Lösung

\int_{0}^{4} \frac{8}{7 x + 6} d x

\frac{8 ( 2 34 - 2 6 )}{7}

Dezimale

7.72905 \dots

Schritte zur Lösung

\int_{0}^{4} \frac{8}{7 x + 6} d x

Entferne die Konstante:

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

= 8 \cdot \int_{0}^{4} \frac{1}{7 x + 6} d x

Wende U-Substitution an

= 8 \cdot \int_{6}^{34} \frac{1}{7 u} d u

Entferne die Konstante:

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

= 8 \cdot \frac{1}{7} \cdot \int_{6}^{34} \frac{1}{u} d u

Wende die Potenzregel an

= 8 \cdot \frac{1}{7} [2 u^{\frac{1}{2}}]_{6}^{34}

Vereinfache

8 \cdot \frac{1}{7} [2 u^{\frac{1}{2}}]_{6}^{34} : \frac{8}{7} [2 u]_{6}^{34}

= \frac{8}{7} [2 u]_{6}^{34}

Berechne die Grenzen:

234 - 26

= \frac{8}{7} (234 - 26)

Vereinfache

= \frac{8 ( 2 34 - 2 6 )}{7}

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