6sinx

6sinx

Input
6 sin(x)
Alternate form
3 i e^(-i x) – 3 i e^(i x)
Roots
x = pi n, n element Z
Series expansion at x=0
6 x – x^3 + x^5/20 + O(x^6)
(Taylor series)
Derivative
d/dx(6 sin(x)) = 6 cos(x)
Indefinite integral
integral 6 sin(x) dx = -6 cos(x) + constant
Global maxima
max{6 sin(x)} = 6 at x = 2 pi n + pi/2 for integer n
Definite integral over a half-period
integral_0^pi 6 sin(x) dx = 12
Definite integral mean square
integral_0^(2 pi) (18 sin^2(x))/pi dx = 18

Leave a Reply

Your email address will not be published.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