Let f(x) = max. `{sinx , cosx , (1)/(2)}` , then area of the region bounded by the curves y = f(x) , x-axis , y-axis and `x = 2pi`

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