What is the integral from 0 to 2pi of x^2 ?

The integral from 0 to 2pi of x^2 is (8pi^3)/3

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integral from 0 to 2pi of x^2

\int_{0}^{2 π} x^{2} d x

\frac{8 π ^{3}}{3}

Decimal

82.68340 \dots

Solution steps

\int_{0}^{2 π} x^{2} d x

Apply the Power Rule

= [\frac{x ^{3}}{3}]_{0}^{2 π}

Compute the boundaries:

\frac{8 π ^{3}}{3}

= \frac{8 π ^{3}}{3}

What is the integral from 0 to 2pi of x^2 ?
The integral from 0 to 2pi of x^2 is (8pi^3)/3