2cos^2x
| Input |
|---|
| 2 cos^2(x) |
| Roots |
| x = pi n – pi/2, n element Z |
| Series expansion at x=0 |
| 2 – 2 x^2 + (2 x^4)/3 + O(x^5) (Taylor series) |
| Derivative |
| d/dx(2 cos^2(x)) = -4 sin(x) cos(x) |
| Indefinite integral |
| integral 2 cos^2(x) dx = x + sin(x) cos(x) + constant |
| Definite integral over a half-period |
| integral_0^(pi/2) 2 cos^2(x) dx = pi/2~~1.5708 |
| Definite integral over a period |
| integral_0^pi 2 cos^2(x) dx = pi~~3.14159 |
| Definite integral mean square |
| integral_0^pi (4 cos^4(x))/pi dx = 3/2 = 1.5 |