- #1
transmini
- 81
- 1
For part of a proof of a differential equations equivalence, we needed to use that $$\int_0^t [\int_0^s g(\tau,\phi(\tau))\space d\tau]\space ds = \int_0^t [\int_\tau^t ds]\space g(\tau,\phi(\tau))\space d\tau$$
I understand that the order is being changed to integrate with respect to s first instead of tau, however I don't understand what's happening with the limits of integration. It has something to do with changing the order of integration but I can't follow it if someone could help show the steps between that equality.
In case it is needed, g is a continuous function
I understand that the order is being changed to integrate with respect to s first instead of tau, however I don't understand what's happening with the limits of integration. It has something to do with changing the order of integration but I can't follow it if someone could help show the steps between that equality.
In case it is needed, g is a continuous function