What is the integral from 1 to x of y^{b-1} ?

The integral from 1 to x of y^{b-1} is (x^b-1)/b

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integral from 1 to x of y^{b-1}

\int_{1}^{x} y^{b - 1} d y

\frac{x ^{b} - 1}{b}

Solution steps

\int_{1}^{x} y^{b - 1} d y

Apply the Power Rule

: [\frac{y ^{b}}{b}]_{1}^{x}

= [\frac{y ^{b}}{b}]_{1}^{x}

Compute the boundaries:

\frac{x ^{b}}{b} - \frac{1}{b}

= \frac{x ^{b}}{b} - \frac{1}{b}

Simplify

= \frac{x ^{b} - 1}{b}

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What is the integral from 1 to x of y^{b-1} ?
The integral from 1 to x of y^{b-1} is (x^b-1)/b