Direction : Consider the following for the items that follow :

The area bounded by the parabola y² = kx and the line x = k, where k > 0, is 4/3 square units.

What is the area of the parabola bounded by the latus rectum? 

What is the area between the curve f(x) = x |x| and x-axis for x = [-1, 1]?

For what value of m with m < 0, is the area bounded by the lines y = x, y = mx and x = 2 equal to 3 ?

What is the area of the region (in the first quadrant) bounded by y = $\sqrt{1−\text{x}^2}$, y = x and y = 0 ?