Integrating v^-2 and Comparing Solutions for vi to v and t to 0

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The book is getting the same answer as you, but they are writing it as -1/v+1/vi = -3t. So the only difference is the way it is written. In summary, the integral from v=vi to v of v^-2dv = -3 integral from t=0 to t of dt. The book and the student both get the same answer, but the book writes it as -1/v+1/vi = -3t, while the student writes it as -1/v + C = -3t. The only difference is the way it is written.
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atypical
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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.
 
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atypical said:

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 vi to v, so you can't really get C.

your integral on the left works out as

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

FAQ: Integrating v^-2 and Comparing Solutions for vi to v and t to 0

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