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

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

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

\int_{0}^{2 π} sin^{3} (x) d x

0

Solution steps

\int_{0}^{2 π} sin^{3} (x) d x

Compute the indefinite integral:

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

Compute the boundaries:

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

= - \frac{2}{3} - (- \frac{2}{3})

Simplify

= 0

\int x^{3} + 2 d x

x \to 15 lim (x + 3)

\int \frac{4 - x}{( x + 2 ) ( x ^{2} + 2 )} d x

\frac{\partial}{\partial y} ((x + y) e^{y})

x \frac{d y}{d x} - 3 y = x^{4}

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