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

解

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

\frac{l}{5}

解答ステップ

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

簡素化

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

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

定数を除く:

\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

べき乗則を適用する

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

簡素化

\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}}

限度を計算する:

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

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

簡素化

= \frac{l}{5}