What is the integral from 0 to 5 of x((2x)/(25)) ?

The integral from 0 to 5 of x((2x)/(25)) is 10/3

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integral from 0 to 5 of x((2x)/(25))

\int_{0}^{5} x (\frac{2 x}{25}) d x

\frac{10}{3}

Decimal Notation

3.33333 \dots

Solution steps

\int_{0}^{5} x \frac{2 x}{25} d x

Take the constant out:

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

= \frac{2}{25} \cdot \int_{0}^{5} xx d x

Simplify

xx : x^{2}

= \frac{2}{25} \cdot \int_{0}^{5} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{5}

= \frac{2}{25} [\frac{x ^{3}}{3}]_{0}^{5}

Compute the boundaries:

\frac{125}{3}

= \frac{2}{25} \cdot \frac{125}{3}

Simplify

= \frac{10}{3}

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What is the integral from 0 to 5 of x((2x)/(25)) ?
The integral from 0 to 5 of x((2x)/(25)) is 10/3