What is the integral from 1 to 2^{1/n of}x^{n-1} ?

The integral from 1 to 2^{1/n of}x^{n-1} is 1/n

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integral from 1 to 2^{1/n of}x^{n-1}

\int_{1}^{2^{\frac{1}{n}}} x^{n - 1} d x

\frac{1}{n}

Solution steps

\int_{1}^{2^{\frac{1}{n}}} x^{n - 1} d x

Apply the Power Rule

: [\frac{x ^{n}}{n}]_{1}^{2^{\frac{1}{n}}}

= [\frac{x ^{n}}{n}]_{1}^{2^{\frac{1}{n}}}

Compute the boundaries:

\frac{1}{n}

= \frac{1}{n}

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What is the integral from 1 to 2^{1/n of}x^{n-1} ?
The integral from 1 to 2^{1/n of}x^{n-1} is 1/n