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

Explanation

To solve the problem, we need to find the area bounded by the function \( f(x) = \max(\sin x, \cos x, \frac{1}{2}) \) from \( x = 0 \) to \( x = 2\pi \). We will break this down step by step.

### Step 1: Identify the function \( f(x) \)

The function \( f(x) \) is defined as the maximum of \( \sin x \), \( \cos x \), and \( \frac{1}{2} \). We need to determine where each of these functions is greater than the others in the interval \( [0, 2\pi] \).

### Step 2: Find critical points

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