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

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

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integral from 0 to 2pi of sin^3(t)

\int_{0}^{2 π} sin^{3} (t) d t

0

Solution steps

\int_{0}^{2 π} sin^{3} (t) d t

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

= 0

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\int_{0}^{3} \frac{3}{3 - x} d x

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