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

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

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

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

0

Solution steps

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

Compute the indefinite integral:

\int cos^{2} (t) sin (t) d t = - \frac{cos ^{3} ( t )}{3} + C

Compute the boundaries:

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

= - \frac{1}{3} - (- \frac{1}{3})

Simplify

= 0

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