Indefinite Integration Problem

1. Oct 22, 2005

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" [Broken]

http://img457.imageshack.us/img457/2315/solution9zq.jpg" [Broken]

Thanks

Last edited by a moderator: May 2, 2017
2. Oct 22, 2005

Tide

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

3. Oct 23, 2005

opticaltempest

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

4. Oct 23, 2005

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.

5. Oct 25, 2005

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" [Broken]

http://img440.imageshack.us/img440/5108/solution20jn.jpg" [Broken]

Thanks

Last edited by a moderator: May 2, 2017