2cosx-1
| Input |
|---|
| 2 cos(x) – 1 |
| Alternate form |
| e^(-i x) + e^(i x) – 1 |
| Series expansion at x=0 |
| 1 – x^2 + x^4/12 + O(x^6) (Taylor series) |
| Derivative |
| d/dx(2 cos(x) – 1) = -2 sin(x) |
| Indefinite integral |
| integral (-1 + 2 cos(x)) dx = 2 sin(x) – x + constant |
| Global maxima |
| max{2 cos(x) – 1} = 1 at x = 2 pi n for integer n |
| Definite integral over a half-period |
| integral_0^pi (-1 + 2 cos(x)) dx = -pi~~-3.14159 |
| Definite integral over a period |
| integral_0^(2 pi) (-1 + 2 cos(x)) dx = -2 pi~~-6.28319 |
| Definite integral mean square |
| integral_0^(2 pi) (-1 + 2 cos(x))^2/(2 pi) dx = 3 |