If `f(x)=` maximum `(sinx,cosx,1/2)` and the area bounded by `y=f(x),x`- axis, `y`- axis and `x=2pi` be `lamda(pi)/12+sqrt(2)+sqrt(3)` sq. units then the value of `lamda` is

Answer

5

Explanation

Required area
`=int_(0)^((pi)/4) cos xdx+int_((pi)/4)^((5pi)/6)sin x dx+int_((5pi)/6)^((5pi)/3) 1/2 x + int_((5pi)/6)^(2pi) cos xdx`
`=1/(sqrt(2))+((sqrt(3))/2+1/(sqrt(2)))+(5pi)/12+(sqrt(3))/2`
`=(5pi)/12+sqrt(2)+sqrt(3)` sq. units