What is the integral from 0 to l of ((x/l)^2)^2 ?

The integral from 0 to l of ((x/l)^2)^2 is l/5

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

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

\frac{l}{5}

Solution steps

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

Simplify

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

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

Take the constant out:

\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

Apply the Power Rule

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

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

Simplify

\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}}

Compute the boundaries:

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

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

Simplify

= \frac{l}{5}

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What is the integral from 0 to l of ((x/l)^2)^2 ?
The integral from 0 to l of ((x/l)^2)^2 is l/5