Cos^4x
| Input |
|---|
| cos^4(x) |
| Roots |
| x = pi n – pi/2, n element Z |
| Series expansion at x=0 |
| 1 – 2 x^2 + (5 x^4)/3 + O(x^6) (Taylor series) |
| Derivative |
| d/dx(cos^4(x)) = -4 sin(x) cos^3(x) |
| Indefinite integral |
| integral cos^4(x) dx = 1/32 (12 x + 8 sin(2 x) + sin(4 x)) + constant |
| Definite integral over a half-period |
| integral_0^pi cos^4(x) dx = (3 pi)/8~~1.1781 |
| Definite integral over a period |
| integral_0^(2 pi) cos^4(x) dx = (3 pi)/4~~2.35619 |
| Definite integral mean square |
| integral_0^(2 pi) (cos^8(x))/(2 pi) dx = 35/128~~0.273438 |