Cosx^2 integral
| Indefinite integral |
|---|
| integral cos^2(x) dx = 1/2 (x + sin(x) cos(x)) + constant |
| Expanded form of the integral |
| x/2 + 1/2 sin(x) cos(x) + constant |
| Series expansion of the integral at x=0 |
| x – x^3/3 + x^5/15 + O(x^6) (Taylor series) |
| Series expansion of the integral at x=∞ |
| 1/4 ((2 x + O((1/x)^13)) + sin(2 x)) |
| Definite integral over a half-period |
| integral_0^(pi/2) cos^2(x) dx = pi/4~~0.785398 |
| Definite integral over a period |
| integral_0^pi cos^2(x) dx = pi/2~~1.5708 |
| Definite integral mean square |
| integral_0^pi (cos^4(x))/pi dx = 3/8 = 0.375 |