- #1

utkarshakash

Gold Member

- 855

- 13

## 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!