integral from 9 to 16 of 5/(sqrt(x^3))

Lösung

\int_{9}^{16} \frac{5}{x ^{3}} d x

\frac{5}{6}

Dezimale

0.83333 \dots

Schritte zur Lösung

\int_{9}^{16} \frac{5}{x ^{3}} d x

Entferne die Konstante:

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

= 5 \cdot \int_{9}^{16} \frac{1}{x ^{3}} d x

Wende Exponentenregel an:

(a^{n})^{m} = a^{n \cdot m}

x^{3} = x^{\frac{3}{2}}

= 5 \cdot \int_{9}^{16} \frac{1}{x ^{\frac{3}{2}}} d x

Wende die Potenzregel an

= 5 [- \frac{2}{x}]_{9}^{16}

Berechne die Grenzen:

\frac{1}{6}

= 5 \cdot \frac{1}{6}

Vereinfache

= \frac{5}{6}

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