The area of the region enclosed by the curve f x = max sin x , cos x , - π ≤ x ≤ π and the x - axis is

Step-by-step solution

Plotting the required diagram we get, Now from diagram we can say that, sin x is maximum for x ∈ - π , - 3 π 4 ∪ π 4 , π and cos x is maximum for x ∈ - 3 π 4 , - π 2 ∪ - π 2 , π 4 So, area of the region is given by, A = ∫ - π - 3 π 4 sin x d x + ∫ π 4 π sin x d x + ∫ - 3 π 4 - π 2 cos x d x + ∫ - π 2 π 4 cos x d x ⇒ A = 1 2 - 1 + 1 + 1 2 + - 1 + 1 2 + 1 2 + 1 ⇒ A = 2 + 2 2 + 2