To estimate the area under the graph of f(x) = 2/x from x = 1 to x = 2 using four approximating rectangles and right endpoints, follow these steps:

1. First, determine the width of each rectangle. The interval from 1 to 2 is divided into 4 equal parts, so each rectangle has a width of (2-1)/4 = 0.25.

2. Next, find the right endpoints. These are the x-values where the right side of each rectangle touches the curve. Since we're starting at x = 1 and each rectangle has a width of 0.25, the right endpoints are x = 1.25, 1.5, 1.75, and 2.

3. Now, calculate the height of each rectangle. The height is the value of the function f(x) = 2/x at the right endpoint. So, the heights are f(1.25) = 2/1.25 = 1.6, f(1.5) = 2/1.5 = 1.3333, f(1.75) = 2/1.75 = 1.1429, and f(2) = 2/2 = 1.

4. Multiply the width and height of each rectangle to find its area. The areas are 0.25*1.6 = 0.4, 0.25*1.3333 = 0.3333, 0.25*1.1429 = 0.2857, and 0.25*1 = 0.25.

5. Finally, add up the areas of all the rectangles to estimate the total area under the curve. The total area is 0.4 + 0.3333 + 0.2857 + 0.25 = 1.2690.

So, the estimated area under the graph of f(x) = 2/x from x = 1 to x = 2 using four approximating rectangles and right endpoints is approximately 1.2690.

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To estimate the area under the graph of f(x) = 2/x from x = 1 to x = 2 using four approximating rectangles and right endpoints, follow these steps:

1. First, determine the width of each rectangle. The interval from 1 to 2 is divided into 4 equal parts, so each rectangle has a width of (2-1)/4 = 0.25.

2. Next, find the right endpoints. These are the x-values where the right side of each rectangle touches the curve. Since we're starting at x = 1 and each rectangle has a width of 0.25, the right endpoints are x = 1.25, 1.5, 1.75, and 2.

3. Now, calculate the height of each rectangle. The height is the value of the function f(x) = 2/x at the right endpoint. So, the heights are f(1.25) = 2/1.25 = 1.6, f(1.5) = 2/1.5 = 1.3333, f(1.75) = 2/1.75 = 1.1429, and f(2) = 2/2 = 1.

4. Multiply the width and height of each rectangle to find its area. The areas are 0.25*1.6 = 0.4, 0.25*1.3333 = 0.3333, 0.25*1.1429 = 0.2857, and 0.25*1 = 0.25.

5. Finally, add up the areas of all the rectangles to estimate the total area under the curve. The total area is 0.4 + 0.3333 + 0.2857 + 0.25 = 1.2690.

So, the estimated area under the graph of f(x) = 2/x from x = 1 to x = 2 using four approximating rectangles and right endpoints is approximately 1.2690.

Knowee AI · Accepted Answer

To estimate the area under the graph of f(x) = 2/x from x = 1 to x = 2 using four approximating rectangles and right endpoints, follow these steps:

1. First, determine the width of each rectangle. The interval from 1 to 2 is divided into 4 equal parts, so each rectangle has a width of (2-1)/4 = 0.25.

2. Next, find the right endpoints. These are the x-values where the right side of each rectangle touches the curve. Since we're starting at x = 1 and each rectangle has a width of 0.25, the right endpoints are x = 1.25, 1.5, 1.75, and 2.

3. Now, calculate the height of each rectangle. The height is the value of the function f(x) = 2/x at the right endpoint. So, the heights are f(1.25) = 2/1.25 = 1.6, f(1.5) = 2/1.5 = 1.3333, f(1.75) = 2/1.75 = 1.1429, and f(2) = 2/2 = 1.

4. Multiply the width and height of each rectangle to find its area. The areas are 0.25*1.6 = 0.4, 0.25*1.3333 = 0.3333, 0.25*1.1429 = 0.2857, and 0.25*1 = 0.25.

5. Finally, add up the areas of all the rectangles to estimate the total area under the curve. The total area is 0.4 + 0.3333 + 0.2857 + 0.25 = 1.2690.

So, the estimated area under the graph of f(x) = 2/x from x = 1 to x = 2 using four approximating rectangles and right endpoints is approximately 1.2690.

Estimate the area under the graph of f(x) = 2/x from x = 1 to x = 2 using four approximating rectangles and right endpoints. (Round your answer to four decimal places.)

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