The discussion revolves around a double integral of a function that depends on the difference between two variables, specifically the expression \(\int_a^b \int_a^b f(x-y)\, dxdy\). Participants are exploring potential simplifications, particularly the possibility of reducing the expression to a one-dimensional integral.
The discussion is ongoing, with participants providing guidance on the change of variables technique while also expressing uncertainty about its application. There is recognition of the need to correctly apply the Jacobian factor and adjust the limits of integration, indicating a productive exploration of the topic.
Participants are navigating the complexities of double integrals and the implications of variable transformations, highlighting a lack of consensus on the best approach to simplify the integral.
Irid said:Homework Statement
Consider a function which depends only on a difference between two variables, and integrate it with respect to both:
[tex] \int_a^b \int_a^b f(x-y)\, dxdy[/tex]
Is there any way to simplify this expression, like reducing it into a 1-D integral?
Irid said:This gives me
[tex]dxdy = (dv^2-du^2)/4[/tex]
and I don't see how this makes the integral any easier