integral from 0 to 4 of 2/(sqrt(9x+8))

Lösung

\int_{0}^{4} \frac{2}{9 x + 8} d x

\frac{2 ( 4 11 - 4 2 )}{9}

Dezimale

1.69103 \dots

Schritte zur Lösung

\int_{0}^{4} \frac{2}{9 x + 8} d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{4} \frac{1}{9 x + 8} d x

Wende U-Substitution an

= 2 \cdot \int_{8}^{44} \frac{1}{9 u} d u

Entferne die Konstante:

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

= 2 \cdot \frac{1}{9} \cdot \int_{8}^{44} \frac{1}{u} d u

Wende die Potenzregel an

= 2 \cdot \frac{1}{9} [2 u^{\frac{1}{2}}]_{8}^{44}

Vereinfache

2 \cdot \frac{1}{9} [2 u^{\frac{1}{2}}]_{8}^{44} : \frac{2}{9} [2 u]_{8}^{44}

= \frac{2}{9} [2 u]_{8}^{44}

Berechne die Grenzen:

411 - 42

= \frac{2}{9} (411 - 42)

Vereinfache

= \frac{2 ( 4 11 - 4 2 )}{9}

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