Question

The value of ` int _(0)^(pi) (dx)/(5+4 cos x ) ` is
A. `2pi`
B. `(3pi)/2`
C. `(5pi)/4`
D. `pi/3`

Answer 1

Correct Answer - D
Put tan `(x)/(2)=t`
`therefore " " dx=(2dt)/(1+t^(2))` and `cos x = (1-t^(2))/(1+t^(2))`
`therefore " " int_(0)^(pi)(dx)/(5+4 cos x)=int_(0)^(oo)(2dt)/(9+t^(2))`
`= [(2)/(3)tan^(-1)((t)/(3))]_(0)^(oo)=(2)/(3)(tan^(-1)oo-0)=(pi)/(3)`.