a.

b. What if you were not restricted to using just rectangles to fill up the space between the curve and the x-axis? Suggest a different geometric shape that you think might give us a more accurate estimate for this area? Justify why you think your new geometric shape would yield a more accurate result.
c.

d. Is your estimate too small or too large? Will this method always produce an estimate that is too small or large? Under what conditions will the estimate using trapezoids ever be too small or large?

In this Exploration, we'll consider a specific case now in which we want to estimate the area between the function y=x and the x-axis on the interval [0, 3]. 8 6 4 2 0 0 a=0 1 As you learned in lesson 2, this area can also be thought of as the value of the definite integral x dx. 2 3 b=3