integral from 1/2 to 1 of 8/(x^3)

Lösung

\int_{\frac{1}{2}}^{1} \frac{8}{x ^{3}} d x

12

Schritte zur Lösung

\int_{\frac{1}{2}}^{1} \frac{8}{x ^{3}} d x

Entferne die Konstante:

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

= 8 \cdot \int_{\frac{1}{2}}^{1} \frac{1}{x ^{3}} d x

Wende die Potenzregel an

= 8 [- \frac{1}{2 x ^{2}}]_{\frac{1}{2}}^{1}

Berechne die Grenzen:

\frac{3}{2}

= 8 \cdot \frac{3}{2}

Vereinfache

= 12

\int_{1}^{2} (2 x^{2} + 3) d x

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