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FInd this integral

  • #1
utkarshakash
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Homework Statement


Evaluate [itex]\displaystyle \int_0^{\pi} \log (1+a\cos x) dx[/itex]

Homework Equations



The Attempt at a Solution


Using Leibnitz's Rule,
F'(a)=[itex]\displaystyle \int_0^{\pi} \dfrac{\cos x}{1+a \cos x} dx [/itex]

Now, If I assume sinx=t, then the above integral changes to
[itex]\displaystyle \int_0^{0} \dfrac{dt}{1+a \sqrt{1-t^2}} [/itex]

Since both the limits are zero now, shouldn't the value of integral be 0! :confused:
 

Answers and Replies

  • #2
haruspex
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[itex]\displaystyle \int_0^{0} \dfrac{dt}{1+a \sqrt{1-t^2}} [/itex]

Since both the limits are zero now, shouldn't the value of integral be 0! :confused:
No. For one thing, the use of the square root function hides the fact that cos(t) will change sign over the range. Split it into two integrals to be safe.
 

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