1+2cosx
| Input |
|---|
| 1 + 2 cos(x) |
| Alternate form |
| e^(-i x) + e^(i x) + 1 |
| Series expansion at x=0 |
| 3 – x^2 + x^4/12 + O(x^6) (Taylor series) |
| Derivative |
| d/dx(1 + 2 cos(x)) = -2 sin(x) |
| Indefinite integral |
| integral (1 + 2 cos(x)) dx = x + 2 sin(x) + constant |
| Global maxima |
| max{1 + 2 cos(x)} = 3 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 |