integral from 1 to 9 of 1/(2sqrt(x))

Lösung

\int_{1}^{9} \frac{1}{2 x} d x

2

Schritte zur Lösung

\int_{1}^{9} \frac{1}{2 x} d x

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{1}^{9} \frac{1}{x} d x

Wende die Potenzregel an

= \frac{1}{2} [2 x^{\frac{1}{2}}]_{1}^{9}

Wende Radikal Regel an:

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

= \frac{1}{2} [2 x]_{1}^{9}

Berechne die Grenzen:

4

= \frac{1}{2} \cdot 4

Vereinfache

= 2

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