2sin2x
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 |