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

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

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

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

0

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - 0

Simplify

= 0

\int_{0}^{\frac{π}{6}} x cos (3 x) d x

\int_{0}^{1} π (4 x^{2})^{2} d x

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

\int_{0}^{3} 2 x - x^{2} d x

\int_{1}^{3} (t^{2} - t + 6) d t

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