Indefinite integral
integral sin(X) 3 dX = -3 cos(X) + constant
Alternate form of the integral
-3/2 e^(-i X) – (3 e^(i X))/2 + constant
Series expansion of the integral at X=0
-3 + (3 X^2)/2 – X^4/8 + O(X^6)
(Taylor series)
Definite integral over a half-period
integral_0^pi 3 sin(X) dX = 6
Definite integral mean square
integral_0^(2 pi) (9 sin^2(X))/(2 pi) dX = 9/2 = 4.5