integral from 2 to x of-2/(t^3)

Lösung

\int_{2}^{x} - \frac{2}{t ^{3}} d t

\frac{1}{x ^{2}} - \frac{1}{4}

Schritte zur Lösung

\int_{2}^{x} - \frac{2}{t ^{3}} d t

Entferne die Konstante:

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

= - 2 \cdot \int_{2}^{x} \frac{1}{t ^{3}} d t

Wende die Potenzregel an

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

Berechne die Grenzen:

- \frac{1}{2 x ^{2}} + \frac{1}{8}

= - 2 (- \frac{1}{2 x ^{2}} + \frac{1}{8})

Vereinfache

= \frac{1}{x ^{2}} - \frac{1}{4}

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