integral from 2 to 10 of 1/(sqrt(5x-1))

Lösung

\int_{2}^{10} \frac{1}{5 x - 1} d x

\frac{8}{5}

Dezimale

1.6

Schritte zur Lösung

\int_{2}^{10} \frac{1}{5 x - 1} d x

Wende U-Substitution an

= \int_{9}^{49} \frac{1}{5 u} d u

Entferne die Konstante:

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

= \frac{1}{5} \cdot \int_{9}^{49} \frac{1}{u} d u

Wende die Potenzregel an

= \frac{1}{5} [2 u^{\frac{1}{2}}]_{9}^{49}

Wende Radikal Regel an:

a^{\frac{1}{n}} = n a

= \frac{1}{5} [2 u]_{9}^{49}

Berechne die Grenzen:

8

= \frac{1}{5} \cdot 8

Vereinfache

= \frac{8}{5}

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