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

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

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integral from 0 to 2pi of θ^2

\int_{0}^{2 π} θ^{2} d θ

\frac{8 π ^{3}}{3}

Decimal

82.68340 \dots

Solution steps

\int_{0}^{2 π} θ^{2} d θ

Apply the Power Rule

: [\frac{θ ^{3}}{3}]_{0}^{2 π}

= [\frac{θ ^{3}}{3}]_{0}^{2 π}

Compute the boundaries:

\frac{8 π ^{3}}{3}

= \frac{8 π ^{3}}{3}

\int_{0}^{\frac{π}{2}} (1 - cos (x))^{2} d x

\int_{0}^{5} \frac{x + 1}{2} d x

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

\int_{- 4}^{4} 1 d x

\int_{- π}^{π} x^{6} sin (x) d x

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