Integrating a Definite Integral with Trigonometric Functions

[utkarsh009]

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!

 

[Mark44]

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.

I couldn't figure out what to do next... Please help!

 

[utkarsh009]

Oh yes... By mistake i typed the integration symbol after it. Cosec a should be inside the integral. So, how should i proceed??

 

[Mark44]

I would try a different substitution -- let t = cos(a).That should get you an integral that's easier to do.

 

[utkarsh009]

Oh yah... Thanks ... I solved it... But have a look at this file... I couldn't get an answer for this...