Integrate cos4x

Integrate cos4x

Indefinite integral
integral cos(4 x) dx = 1/4 sin(4 x) + constant
Series expansion of the integral at x=0
x – (8 x^3)/3 + (32 x^5)/15 + O(x^6)
(Taylor series)
Definite integral
integral_0^(pi/8) cos(4 x) dx = 1/4 = 0.25
Definite integral mean square
integral_0^(pi/2) (2 cos^2(4 x))/pi dx = 1/2 = 0.5

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