2sinxcosx=
| Input |
|---|
| 2 sin(x) cos(x) |
| Roots |
| x = (pi n)/2, n element Z |
| Series expansion at x=0 |
| 2 x – (4 x^3)/3 + (4 x^5)/15 + O(x^6) (Taylor series) |
| Derivative |
| d/dx(2 sin(x) cos(x)) = 2 cos(2 x) |
| Indefinite integral |
| integral 2 cos(x) sin(x) dx = -1/2 cos(2 x) + constant |
| Definite integral over a half-period |
| integral_0^(pi/2) 2 cos(x) sin(x) dx = 1 |
| Definite integral mean square |
| integral_0^pi (4 cos^2(x) sin^2(x))/pi dx = 1/2 = 0.5 |