Cosx * sinx

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

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