Use the given function values to estimate the area under the curve using left-endpoint and right-endpoint evaluation. Round to two decimal places. 0.0
A) Left-endpoint estimate is ; right-endpoint estimate is
B) Left-endpoint estimate is ; right-endpoint estimate is
C) Left-endpoint estimate is ; right-endpoint estimate is
D) Left-endpoint estimate is ; right-endpoint estimate is

Question

Use the given function values to estimate the area under the curve using left-endpoint and right-endpoint evaluation. Round to two decimal places.  0.0                   
A) Left-endpoint estimate is ; right-endpoint estimate is 
B) Left-endpoint estimate is ; right-endpoint estimate is 
C) Left-endpoint estimate is ; right-endpoint estimate is 
D) Left-endpoint estimate is ; right-endpoint estimate is

Quizplus · Accepted Answer

The left-endpoint and right-endpoint estimates both represent approximations of the area under the curve by approximating the height of the rectangles using either the left or the right endpoint value of each interval. To calculate the estimated area using either method, we sum up the areas of all the rectangles formed. The estimate obtained by adding the areas of rectangles obtained using left endpoints is always an underestimate of the true area, whereas that obtained by adding the areas of rectangles obtained using right-endpoint provides an overestimate of the true area. The best estimate of the true area is expected to lie somewhere between the two estimates. Therefore, we can choose the estimate that lies midway between the two endpoint estimates, which in this case is C.

Use the Given Function Values to Estimate the Area Under