1 + cos2x
| Input |
|---|
| 1 + 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(1 + cos(2 x)) = -2 sin(2 x) |
| Indefinite integral |
| integral (1 + cos(2 x)) dx = x + sin(x) cos(x) + constant |
| Global maxima |
| max{1 + cos(2 x)} = 2 at x = pi n for integer n |
| Definite integral over a half-period |
| integral_0^(pi/2) (1 + cos(2 x)) dx = pi/2~~1.5708 |
| Definite integral over a period |
| integral_0^pi (1 + cos(2 x)) dx = pi~~3.14159 |
| Definite integral mean square |
| integral_0^pi (1 + cos(2 x))^2/pi dx = 3/2 = 1.5 |