We will investigate different numerical methods of estimating the area between a curve and the x-axis. We will look at dividing the area into rectangles, using either the upper value, lower value or midpoint as the height of the rectangle, or trapeziums. You can change the endpoints of the interval by moving points A and B. You can investigate different polynomials by changing the a,b, and c sliders for the quadratic. You can change the number of sub intervals by changing the n slider.

What happens to the accuracy of the estimate as you increase the number of subintervals?
Which of the methods appears to be the most accurate? Why do you think this is?
Could you use any other shapes to divide the area?
Do all the intervals have to be equal width?