Change of variable...

eljose

let be the integral:

f(x+{y}) where {y}=y iff y>0 and -y iff y<0, then we make the change of variable x+{y}=u x=v then what would be the value of Jacobian?

matt grime

|y| isn't differentiable so one cannot do it directly. but one may split the region of integration into the regions where y is positive and negative and thence do the integral.