Question

I'm not sure I completely understand why the following differential / integral manipulation is mathematically correct.

Answer 1

\[\int\limits_{0}^{t}L \frac{ di(t) }{ dt } i(t) dt = \int\limits_{0}^{i(t)}L i(t) di(t) \]

Answer 2

What I don't understand is why the upper bound is i(t) and not t while the right and left hand side of the equation remain equivalent.

Answer 3

This is from an electrical engineering book. Thus i(t) is the current as a function of time, thus t > 0

Answer 4

I'm thinking it might be u-substitution

Answer 5

\[u=i(t)\]
\[du=\frac{ di(t) }{ dt }di(t)\]
then change the limits