Integral cos^3x
| Indefinite integral |
|---|
| integral cos^3(x) dx = 1/12 (9 sin(x) + sin(3 x)) + constant |
| Expanded form of the integral |
| (3 sin(x))/4 + 1/12 sin(3 x) + constant |
| Series expansion of the integral at x=0 |
| x – x^3/2 + (7 x^5)/40 + O(x^6) (Taylor series) |
| Definite integral |
| integral_0^(pi/2) cos^3(x) dx = 2/3~~0.666667 |
| Definite integral mean square |
| integral_0^(2 pi) (cos^6(x))/(2 pi) dx = 5/16 = 0.3125 |