Question

Use the rectangles to approximate the area of the region. (Round your answer to three decimal places.)

The x y-coordinate plane is given. There is 1 curve, a shaded region, and 4 rectangles on the graph.

• The curve enters the window in the first quadrant, goes down and right becoming less steep, passes through the point (1, 5), passes through the point (5, 1), and exits the window almost horizontally above the x-axis.
• The region below the curve, above the x-axis, and between the values of 1 and 5 on the x-axis is shaded.
• The segments of the x-axis from x = 1 to 2, 2 to 3, 3 to 4, and 4 to 5 serve as the bases of the 4 rectangles.
• The curve passes through the midpoint of the top of each of the 4 rectangles.

f(x) =

5

x

[1, 5]

Give the exact area obtained using a definite integral.

Answer 1

we are given

interval is [1,5]

n=4

Firstly, we will find delta x

Approximate Area:

we can find mid point sum

now, we can plug values

Exact Area:

we can set up integral for area

.............Answer