Checking constant of integration assumptions in indefinite integral

[opticaltempest]

Calc I - Simple Indefinite Integration Problem

Hello,

Here is an indefinite integration problem I have been
working on. Would anyone be willing to check my solution?
Are my assumptions about replacing the C and -C correct?

http://img457.imageshack.us/img457/8933/problem0kw.jpg"

http://img457.imageshack.us/img457/2315/solution9zq.jpg"

Thanks

 

[Tide]

Set up your integrals as definite integrals and the constants will take care of themselves! :)

 

[opticaltempest]

This is my first section on covering integrals so I haven't covered definite integrals yet.

 

[HallsofIvy]

It would make more sense to combine the two constants (and would be much better to use different letters to represent them) into one, then determine its value.

 

[opticaltempest]

I got some more help on this problem today but I am still stuck. It was suggested to
me that after realizing v(0)=v_0 we can come up with

v_0^2 = 2GM(1/R) + C

How can we conclude this?
Why replace the 1/y with 1/R ?Here is the entire solution that was presented to me
--------------------------------------------------

v^2 = 2GM(1/y) + C

then from v(0)=v_0 we would have obtained

[v_0]^2 = 2GM(1/R) + C

C = [v_0]^2 - 2GM(1/R)

so that

v^2 = 2GM(1/y) + [v_0]^2 - 2GM(1/R)

which can be rewritten as

v^2 = [v_0]^2 + 2GM( 1/y - 1/R)
http://img440.imageshack.us/img440/6539/solution14yb.jpg"

http://img440.imageshack.us/img440/5108/solution20jn.jpg"

Thanks