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

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

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

\int_{0}^{2 π} - sin^{3} (x) d x

0

Solution steps

\int_{0}^{2 π} - sin^{3} (x) d x

Compute the indefinite integral:

\int - sin^{3} (x) d x = cos (x) - \frac{1}{3} cos^{3} (x) + C

Compute the boundaries:

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

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

Simplify

= 0

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