2sin^2x

2sin^2x

Input
2 sin^2(x)
Roots
x = pi n, n element Z
Series expansion at x=0
2 x^2 – (2 x^4)/3 + (4 x^6)/45 – (2 x^8)/315 + O(x^9)
(Taylor series)
Derivative
d/dx(2 sin^2(x)) = 4 sin(x) cos(x)
Indefinite integral
integral 2 sin^2(x) dx = x – sin(x) cos(x) + constant
Definite integral over a half-period
integral_0^(pi/2) 2 sin^2(x) dx = pi/2~~1.5708
Definite integral over a period
integral_0^pi 2 sin^2(x) dx = pi~~3.14159
Definite integral mean square
integral_0^pi (4 sin^4(x))/pi dx = 3/2 = 1.5

Leave a Reply

Your email address will not be published.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