Question

Let f(x) = max{x²,(1 – x)²,2x(1 – x)} where 0 ≤ x ≤ 1. Determine the area of the region bounded by the curves y = f(x), x-axis, x = 0, x = 1.

Answer 1

Given curve is

f(x) = max{x², (1 – x)², 2x(1 – x)} 

From the graph, it is clear that

Hence, the required area

= 17/27 sq.u.