CPM Homework Banner

Write and then compute a Riemann sum to estimate the area the curve for given . Choose the number of rectangles so that your answer will be a good approximation of the area. What is the name of the shape of which you calculated the area? Confirm the accuracy of the Riemann sum by calculating the area geometrically. 3-74 HW eTool (Desmos). Homework Help ✎

General form of a left-endpoint Riemann sum:

Hint for choosing the number of rectangles, : While you want to choose a large value for , be mindful that you will use that value to compute .

After all: 

Since , it is recommended (though not necessary) that you choose an that is divisible by .

You should have recognized that this function is a semi-circle with center at the origin and radius . The exact area can be found with geometry.

Use the eTool below to visualize this problem.
Click the link at right for the full version of the eTool: Calc 3-74 HW eTool