Conclude your observations by comparing the left endpoint estimate and the right endpoint estimate to actual area in each case. Generalisze your findings by stating when the left endpoint estimate overestimates and when it underestimates the area under the curve. In your conclusion you need to refer to the shape of the graph (concave up or down) and also comment on the increasing or decreasing property of a function over the given interval. Does the number of subdivisions affect the accuracy of estimation?

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**Aim:** To estimate areas under the curve using the left endpoint estimate and the right endpoint estimate. Then to compare the estimates to the actual area under the curve and to conclude how the error of the approximation is affected by the shape of the curve and the number of intervals. Use your CAS calculator to find the actual area in each case.