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

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

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integral from 0 to 2pi of sin^3(θ)

\int_{0}^{2 π} sin^{3} (θ) d θ

0

Solution steps

\int_{0}^{2 π} sin^{3} (θ) d θ

Compute the indefinite integral:

\int sin^{3} (θ) d θ = - cos (θ) + \frac{cos ^{3} ( θ )}{3} + C

Compute the boundaries:

\int_{0}^{2 π} sin^{3} (θ) d θ = - \frac{2}{3} - (- \frac{2}{3})

= - \frac{2}{3} - (- \frac{2}{3})

Simplify

= 0

\int_{0}^{\frac{π}{3}} sin^{3} (3 x) d x

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