integral from 1 to 5 of ((10)/(x^2))^2

Lösung

\int_{1}^{5} (\frac{10}{x ^{2}})^{2} d x

\frac{496}{15}

Dezimale

33.06666 \dots

Schritte zur Lösung

\int_{1}^{5} (\frac{10}{x ^{2}})^{2} d x

Vereinfache

(\frac{10}{x ^{2}})^{2} : \frac{100}{x ^{4}}

= \int_{1}^{5} \frac{100}{x ^{4}} d x

Entferne die Konstante:

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

= 100 \cdot \int_{1}^{5} \frac{1}{x ^{4}} d x

Wende die Potenzregel an

= 100 [- \frac{1}{3 x ^{3}}]_{1}^{5}

Berechne die Grenzen:

\frac{124}{375}

= 100 \cdot \frac{124}{375}

Vereinfache

= \frac{496}{15}

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