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

reqruied area
`=int_(0)^((pi)/(4))cosxdx+int_((pi)/(4))^((5pi)/(6))sinxdx+int_((5pi)/(6))^((5pi)/(3))(1)/(2)dx+int_((5pi)/(3))^(pi)cosxdx`
`=(1)/(sqrt(2))+((sqrt(3))/(2)+(1)/(sqrt(2)))+(5pi)/(12)+(sqrt(3))/(2)`
`=(5pi)/(12)+sqrt(2)+sqrt(3)sq.` units