What is the integral from 0 to 5 of 1/5 x^5 ?

The integral from 0 to 5 of 1/5 x^5 is 3125/6

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integral from 0 to 5 of 1/5 x^5

\int_{0}^{5} \frac{1}{5} x^{5} d x

\frac{3125}{6}

Decimal

520.83333 \dots

Solution steps

\int_{0}^{5} \frac{1}{5} x^{5} d x

Take the constant out:

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

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

Apply the Power Rule

= \frac{1}{5} [\frac{x ^{6}}{6}]_{0}^{5}

Compute the boundaries:

\frac{15625}{6}

= \frac{1}{5} \cdot \frac{15625}{6}

Simplify

= \frac{3125}{6}

What is the integral from 0 to 5 of 1/5 x^5 ?
The integral from 0 to 5 of 1/5 x^5 is 3125/6