What is the integral from 0 to 1 of ax^a ?

The integral from 0 to 1 of ax^a is a/(a+1)

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integral from 0 to 1 of ax^a

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

\frac{a}{a + 1}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{1}{a + 1}

= a \frac{1}{a + 1}

Simplify

= \frac{a}{a + 1}

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