integral from 10 to x of (10)/(x^2)

Lösung

\int_{10}^{x} \frac{10}{x ^{2}} d x

- \frac{10}{x} + 1

Schritte zur Lösung

\int_{10}^{x} \frac{10}{x ^{2}} d x

Entferne die Konstante:

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

= 10 \cdot \int_{10}^{x} \frac{1}{x ^{2}} d x

Wende die Potenzregel an

= 10 [- \frac{1}{x}]_{10}^{x}

Berechne die Grenzen:

- \frac{1}{x} + \frac{1}{10}

= 10 (- \frac{1}{x} + \frac{1}{10})

Vereinfache

= - \frac{10}{x} + 1

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