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Definite integration problem

  • #1
47
0

Homework Statement


∫dt/(t^2 +2tcos a + 1)
(Limits of the integral are from 0 to 1)
(0<a<π)

Homework Equations




The Attempt at a Solution


Put t=sin a
dt=cosa da
∫dt/(t^2 +2tcos a + 1) = ∫cos a da/(sin^2 a + sin 2a + 1) [ limits of integration changed to 0 to π/2]
= ((cosec a)/2) ∫sin 2a da/(sin^2 a + sin 2a + 1)

I couldn't figure out what to do next... Please help!!
 
Last edited by a moderator:

Answers and Replies

  • #2
33,265
4,965

Homework Statement


∫dt/(t^2 +2tcos a + 1)
(Limits of the integral are from 0 to 1)
(0<a<π)

Homework Equations




The Attempt at a Solution


Put t=sin a
dt=cosa da
∫dt/(t^2 +2tcos a + 1) = ∫cos a da/(sin^2 a + sin 2a + 1) [ limits of integration changed to 0 to π/2]
= ((cosec a)/2) ∫sin 2a da/(sin^2 a + sin 2a + 1)
I don't know what you did in this last step, but you can't bring csc(a) out as if it were a constant.
utkarsh009 said:
I couldn't figure out what to do next... Please help!!
 
  • #3
47
0
Oh yes... By mistake i typed the integration symbol after it. Cosec a should be inside the integral. So, how should i proceed??
 
  • #4
33,265
4,965
I would try a different substitution -- let t = cos(a).That should get you an integral that's easier to do.
 
  • #5
47
0
Oh yah... Thanks ... I solved it... But have a look at this file... I couldn't get an answer for this...
New Doc 1_1.jpg
 

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