Integral sin^3
| Indefinite integral |
|---|
| integral sin^3(x) dx = 1/12 (cos(3 x) – 9 cos(x)) + constant |
| Expanded form of the integral |
| 1/12 cos(3 x) – (3 cos(x))/4 + constant |
| Series expansion of the integral at x=0 |
| -2/3 + x^4/4 + O(x^6) (Taylor series) |
| Definite integral over a half-period |
| integral_0^pi sin^3(x) dx = 4/3~~1.33333 |
| Definite integral mean square |
| integral_0^(2 pi) (sin^6(x))/(2 pi) dx = 5/16 = 0.3125 |