Cosx^2 integral

Cosx^2 integral

Indefinite integral
integral cos^2(x) dx = 1/2 (x + sin(x) cos(x)) + constant
Expanded form of the integral
x/2 + 1/2 sin(x) cos(x) + constant
Series expansion of the integral at x=0
x – x^3/3 + x^5/15 + O(x^6)
(Taylor series)
Series expansion of the integral at x=∞
1/4 ((2 x + O((1/x)^13)) + sin(2 x))
Definite integral over a half-period
integral_0^(pi/2) cos^2(x) dx = pi/4~~0.785398
Definite integral over a period
integral_0^pi cos^2(x) dx = pi/2~~1.5708
Definite integral mean square
integral_0^pi (cos^4(x))/pi dx = 3/8 = 0.375

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