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

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

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

\int_{0}^{2 π} sin (x) cos^{3} (x) d x

0

Solution steps

\int_{0}^{2 π} sin (x) cos^{3} (x) d x

Compute the indefinite integral:

\int sin (x) cos^{3} (x) d x = - \frac{cos ^{4} ( x )}{4} + C

Compute the boundaries:

\int_{0}^{2 π} sin (x) cos^{3} (x) d x = - \frac{1}{4} - (- \frac{1}{4})

= - \frac{1}{4} - (- \frac{1}{4})

Simplify

= 0

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