Cosx * sinx
| Input |
|---|
| cos(x) sin(x) |
| Series expansion at x=0 |
| x – (2 x^3)/3 + (2 x^5)/15 + O(x^6) (Taylor series) |
| Derivative |
| d/dx(cos(x) sin(x)) = cos(2 x) |
| Indefinite integral |
| integral cos(x) sin(x) dx = -1/2 cos^2(x) + constant |
| Definite integral over a half-period |
| integral_0^(pi/2) cos(x) sin(x) dx = 1/2 = 0.5 |
| Definite integral mean square |
| integral_0^pi (cos^2(x) sin^2(x))/pi dx = 1/8 = 0.125 |