Cant understand this transition

[nhrock3]

http://i47.tinypic.com/2lj3uvl.jpg

how did they erased the derivative of I object

how did they change the variable?

 

[rootX]

Substitute P=Li.di/dt in the equation.. dt cancels out

 

[nhrock3]

why they change t to I
on the interval
?

 

[rootX]

why they change t to I
on the interval
?

Because now we are integrating with respect to i as it goes from 0 to I. First, we were integrating with respect to t which was going from 0 to t. It means that as t goes from 0 to t, i goes from 0 to I and that i is dependent on t.

i(t=0) = 0
i(t=t) = I