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

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

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

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

\frac{5}{3}

Decimal Notation

1.66666 \dots

Solution steps

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

Take the constant out:

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

= \frac{1}{25} \cdot \int_{0}^{5} x^{2} d x

Apply the Power Rule

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

= \frac{1}{25} [\frac{x ^{3}}{3}]_{0}^{5}

Compute the boundaries:

\frac{125}{3}

= \frac{1}{25} \cdot \frac{125}{3}

Simplify

= \frac{5}{3}

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