3cos2x

3cos2x

Input
3 cos(2 x)
Roots
x = (pi n)/2 – pi/4, n element Z
Series expansion at x=0
3 – 6 x^2 + 2 x^4 + O(x^6)
(Taylor series)
Derivative
d/dx(3 cos(2 x)) = -6 sin(2 x)
Indefinite integral
integral 3 cos(2 x) dx = 3 sin(x) cos(x) + constant
Global maxima
max{3 cos(2 x)} = 3 at x = pi n for integer n
Definite integral
integral_0^(pi/4) 3 cos(2 x) dx = 3/2 = 1.5
Definite integral mean square
integral_0^pi (9 cos^2(2 x))/pi dx = 9/2 = 4.5

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