1. Sep 15, 2012 #1

   Mdhiggenz

   

   1. The problem statement, all variables and given/known data
   
   Tan∅ dr + 2r d∅=0
   
   2. Relevant equations
   
   
   
   3. The attempt at a solution
   
   ∫1/2r dr +∫1/tan∅ d∅=0
   
   1/2ln(2r)+ln(tan∅)=c
   ln[r(tan∅)]=ln(c)
   
   r(tan∅)=c
   
   the solution in the book says the answer is rsin^2∅=c
   
   Where did I go wrong?
   
   Thank you

    

   Mdhiggenz, Sep 15, 2012
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3. Sep 15, 2012 #2

   Pranav-Arora

   

   Here's your mistake:
   ∫1/tan∅ d∅≠ln(tan∅)

    

   Pranav-Arora, Sep 15, 2012
4. Sep 15, 2012 #3

   Mdhiggenz

   

   Wow I see it would be ∫cos∅/sin∅ d∅ and with some u substitution it would give us ln(sin∅) correct?

    

   Mdhiggenz, Sep 15, 2012
5. Sep 15, 2012 #4

   Pranav-Arora

   

   Yep, that's right but you have done one more mistake.
   ∫1/2r dr≠(1/2)ln(2r). It is equal to (1/2)ln(r).

    

   Pranav-Arora, Sep 15, 2012

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