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I just cannot understand the following transformation, where [tex]\phi(t)[/tex] is the displacement of an optimal path using standard calculus of variations. All functions are defined between 0 and T. [tex]\phi[/tex] equals zero at 0 and T. r is some discount rate, e it the Euler number, t is time.

[tex]\int^{T}_{0}\theta(y(t))e^{-rt}\int^{t}_{0}\phi(\tau)d\tau]dt[/tex]

This should be equal to

[tex]\int^{T}_{0}\int^{T}_{t}\theta(y(\tau))e^{-r\tau}d\tau]\phi(t)]dt[/tex]

If anybody knows the answer, I would be very happy to get some help here.

Thanks in advance!

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# Double Integration change of variables

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