Why does integrating v^-2 give -1/v + 1/vi instead of -1/v + C?

[atypical]

Homework Statement

The integral from v=vi to v of v^-2dv = -3 integral from t=0 to t of dt

Homework Equations

The Attempt at a Solution

I am getting -1/v + C=-3t and the book is getting -1/v+1/vi=-3t. Not quite sure where they are getting 1/vi as I am getting C.

 

[rock.freak667]

The Attempt at a Solution

I am getting -1/v + C=-3t and the book is getting -1/v+1/vi=-3t. Not quite sure where they are getting 1/vi as I am getting C.

Your integral is from v_i to v, so you can't really get C.

your integral on the left works out as

$$\left[ \frac{-1}{v} \right] _{v_i} ^{v} = \frac{-1}{v}- \left( -\frac{-1}{v_i}\right)$$