2sinxcosx=

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

Leave a Reply

Your email address will not be published. Required fields are marked *