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

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

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

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

0

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

= 0

\int_{- π}^{π} e^{x} cos (x) d x

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\int_{1}^{4} \frac{x ^{5} - x}{3 x ^{3}} d x

\int_{1}^{2} \frac{3}{7} x^{3} d x

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