6sinx
| Input |
|---|
| 6 sin(x) |
| Alternate form |
| 3 i e^(-i x) – 3 i e^(i x) |
| Roots |
| x = pi n, n element Z |
| Series expansion at x=0 |
| 6 x – x^3 + x^5/20 + O(x^6) (Taylor series) |
| Derivative |
| d/dx(6 sin(x)) = 6 cos(x) |
| Indefinite integral |
| integral 6 sin(x) dx = -6 cos(x) + constant |
| Global maxima |
| max{6 sin(x)} = 6 at x = 2 pi n + pi/2 for integer n |
| Definite integral over a half-period |
| integral_0^pi 6 sin(x) dx = 12 |
| Definite integral mean square |
| integral_0^(2 pi) (18 sin^2(x))/pi dx = 18 |