Cos^2 2x
| Input |
|---|
| cos^2(2 x) |
| Roots |
| x = (pi n)/2 – pi/4, n element Z |
| Series expansion at x=0 |
| 1 – 4 x^2 + (16 x^4)/3 + O(x^5) (Taylor series) |
| Derivative |
| d/dx(cos^2(2 x)) = -2 sin(4 x) |
| Indefinite integral |
| integral cos^2(2 x) dx = 1/8 (4 x + sin(4 x)) + constant |
| Definite integral over a half-period |
| integral_0^(pi/4) cos^2(2 x) dx = pi/8~~0.392699 |
| Definite integral over a period |
| integral_0^(pi/2) cos^2(2 x) dx = pi/4~~0.785398 |
| Definite integral mean square |
| integral_0^(pi/2) (2 cos^4(2 x))/pi dx = 3/8 = 0.375 |