Mathematics 2000 JAMB Past Questions - Question 34: If the diagram above is the graph y=x², the shaded area is

Correct Answer

C

Explanation

The shaded area in the graph represents the region between the curve y = x² and the x-axis.To find the area of this shaded region, we need to integrate the function y = x² over the appropriate interval.Looking at the graph, we can see that the shaded region is bounded by the x-axis and the curve y = x². The x-values where the curve intersects the x-axis are x = 0 and x = 1.Therefore, the area of the shaded region can be found by integrating the function y = x² from x = 0 to x = 1:∫[0,1] x² dxIntegrating x² with respect to x, we get:(1/3) x³ |[0,1]Substituting the limits of integration, we have:(1/3) (1³ - 0³)(1/3) (1 - 0)(1/3) (1)1/3Therefore, the area of the shaded region is 1/3 square units.