Area under a Curve

Increase the value of n using the slider. As the value of n increases, what can you say about the sum of the areas of the green rectangles, S, in relation to the area of the region bounded by the curve and the x-axis?

Find the exact value of showing your working clearly.

What can you say about the value of in comparison to the area bounded between the curve y = 3x - 0.5x² and the x-axis?