Find the area bounded by the curve y = x(2-x). The x-axis, x = 0 and x = 2.

To find the area bounded by the curve y = x(2-x), the x-axis, x = 0 and x = 2, we need to integrate the function with respect to x from 0 to 2. The function y = x(2-x) is a quadratic equation, which opens downwards and has its vertex at (1, 1). It intersects the x-axis at x = 0 and x = 2, forming a trapezium. To integrate the function, we need to first expand it: y = x(2-x) = 2x - x^2 Then, we integrate it with respect to x from 0 to 2: ∫(2x - x^2)dx, limits 0 to 2 = [x^2 - (x^3)/3] from 0 to 2 = [(2^2) - (2^3)/3] - [(0^2) - (0^3)/3] = [4 - (8/3)] - [0 - 0] = (4/3) sq units Therefore, the area bounded by the curve y = x(2-x), the x-axis, x = 0 and x = 2 is (4/3) sq units.