integral from 0 to l of ((x/l)^2)^2

Lösung

\int_{0}^{l} ((\frac{x}{l})^{2})^{2} d x

\frac{l}{5}

Schritte zur Lösung

\int_{0}^{l} ((\frac{x}{l})^{2})^{2} d x

Vereinfache

((\frac{x}{l})^{2})^{2} : \frac{x ^{4}}{l ^{4}}

= \int_{0}^{l} \frac{x ^{4}}{l ^{4}} d x

Entferne die Konstante:

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

= \frac{1}{l ^{4}} \cdot \int_{0}^{l} x^{4} d x

Wende die Potenzregel an

= \frac{1}{l ^{4}} [\frac{x ^{5}}{5}]_{0}^{l}

Vereinfache

\frac{1}{l ^{4}} [\frac{x ^{5}}{5}]_{0}^{l} : \frac{[ \frac{x ^{5}}{5} ] _{0}^{l}}{l ^{4}}

= \frac{[ \frac{x ^{5}}{5} ] _{0}^{l}}{l ^{4}}

Berechne die Grenzen:

\frac{l ^{5}}{5}

= \frac{\frac{l ^{5}}{5}}{l ^{4}}

Vereinfache

= \frac{l}{5}

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