What is the integral from 0 to 1 of θx^{θ-1} ?

The integral from 0 to 1 of θx^{θ-1} is 1

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integral from 0 to 1 of θx^{θ-1}

\int_{0}^{1} θ x^{θ - 1} d x

1

Solution steps

\int_{0}^{1} θ x^{θ - 1} d x

Take the constant out:

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

= θ \cdot \int_{0}^{1} x^{- 1 + θ} d x

Apply the Power Rule

= θ [\frac{x ^{θ}}{θ}]_{0}^{1}

Compute the boundaries:

\frac{1}{θ}

= θ \frac{1}{θ}

Simplify

= 1

What is the integral from 0 to 1 of θx^{θ-1} ?
The integral from 0 to 1 of θx^{θ-1} is 1