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

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

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

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

0

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

= 0

\int_{- 1}^{0} (x - x^{3}) d x

\int_{2}^{3} (3 x^{2} - 2 x + 7) d x

\int_{0}^{1} (2 - 2 y^{2})^{3} d y

\int_{1}^{4} x - x + 2 d x

\int_{0}^{1} (x + 2)^{3} d x

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