2sin 2x

2sin 2x

Input
2 sin(2 x)
Roots
x = (pi n)/2, n element Z
Series expansion at x=0
4 x – (8 x^3)/3 + (8 x^5)/15 + O(x^6)
(Taylor series)
Derivative
d/dx(2 sin(2 x)) = 4 cos(2 x)
Indefinite integral
integral 2 sin(2 x) dx = -cos(2 x) + constant
Global maxima
max{2 sin(2 x)} = 2 at x = pi n + pi/4 for integer n
Definite integral over a half-period
integral_0^(pi/2) 2 sin(2 x) dx = 2
Definite integral mean square
integral_0^pi (4 sin^2(2 x))/pi dx = 2

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