What is the integral from 0 to 1 of nx^n ?

The integral from 0 to 1 of nx^n is n/(n+1)

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integral from 0 to 1 of nx^n

\int_{0}^{1} n x^{n} d x

\frac{n}{n + 1}

Solution steps

\int_{0}^{1} n x^{n} d x

Take the constant out:

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

= n \cdot \int_{0}^{1} x^{n} d x

Apply the Power Rule

: [\frac{x ^{n + 1}}{n + 1}]_{0}^{1}

= n [\frac{x ^{n + 1}}{n + 1}]_{0}^{1}

Compute the boundaries:

\frac{1}{n + 1}

= n \frac{1}{n + 1}

Simplify

= \frac{n}{n + 1}

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What is the integral from 0 to 1 of nx^n ?
The integral from 0 to 1 of nx^n is n/(n+1)