## anonymous one year ago I'm not sure I completely understand why the following differential / integral manipulation is mathematically correct.

1. anonymous

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

2. anonymous

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.

3. anonymous

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

4. anonymous

I'm thinking it might be u-substitution

5. anonymous

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