Approximate the area under the curve on the given interval using rectangles and left-endpoint evaluation. Round to three decimal places. on ,

Question

Approximate the area under the curve on the given interval using  rectangles and left-endpoint evaluation. Round to three decimal places.  on  ,

Quizplus · Accepted Answer

We need to find the width of each rectangle first. The interval from 2 to 5 is divided into 11 equal subintervals, so the width of each rectangle is Δx = (5-2)/11 = 0.2727 (to four decimal places).

The height of each rectangle is given by the function evaluated at the left endpoint of each subinterval. For example, the height of the first rectangle is f(2) = 0.2.

Using left-endpoint evaluation, we add up the areas of all 11 rectangles:

Area ≈ Δx (f(2) + f(2.2727) + f(2.5455) + ... + f(4.7273))
≈ 0.2727 (0.2 + 0.21 + 0.202 + ... + 0.202)
≈ 0.2189 (rounded to three decimal places)

Therefore, the answer is choice A (0.219).

Approximate the Area Under the Curve on the Given Interval