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

The integral from 0 to 1 of ax^{a-1} is 1

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integral from 0 to 1 of ax^{a-1}

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

1

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{1}{a}

= a \frac{1}{a}

Simplify

= 1

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\int_{0}^{3} 2 y - y^{2} - (y^{2} - 4 y) d y

\int_{0}^{3} (3 t - 1)^{68} d t

What is the integral from 0 to 1 of ax^{a-1} ?
The integral from 0 to 1 of ax^{a-1} is 1