What is the integral from a to b of x^n ?

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

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integral from a to b of x^n

\int_{a}^{b} x^{n} d x

\frac{b ^{n + 1} - a ^{n + 1}}{n + 1}

Solution steps

\int_{a}^{b} x^{n} d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{b ^{n + 1}}{n + 1} - \frac{a ^{n + 1}}{n + 1}

= \frac{b ^{n + 1}}{n + 1} - \frac{a ^{n + 1}}{n + 1}

Simplify

= \frac{b ^{n + 1} - a ^{n + 1}}{n + 1}

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