Use the rectangles in the following graph to approximate the area of the region bounded by , , ,and .

Question

Use the rectangles in the following graph to approximate the area of the region bounded by  ,  ,  ,and  . ​  ​

Quizplus · Accepted Answer

The region is a quarter of a circle with radius 2, so its area is $\frac{1}{4}\pi(2)^2 = \pi$. Looking at the rectangles, we see that the width of each rectangle is $\frac{1}{2}$ and the heights are 1, 2, 2, 2, and 1, respectively. Adding up the areas of the rectangles gives an approximation of $\frac{1}{2}(1+2+2+2+1) = 4$. The best choice is B, which is closest to the true area of $\pi$.

Use the Rectangles in the Following Graph to Approximate the Area