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F of G of X

Geometric figure

line

Properties as a real function

R (all real numbers)

{y element R : y = 0 or (f!=0 and g!=0)}

odd

Derivative

d/dx(f g x) = f g

Indefinite integral

integral f g x dx = 1/2 f g x^2 + constant

Definite integral over a cube of edge length 2 L

integral_(-L)^L integral_(-L)^L integral_(-L)^L f g x dx dg df = 0

Definite integral over a sphere of radius R

integral integral integral_(f^2 + g^2 + x^2<R^2) f g x df dg dx = 0