Area Estimates. Find the following area estimates under the graph of the function y= 1/x. Give your answers as (exact) rational numbers.

Question

 Area Estimates. Find the following area estimates under the graph of the function  Give your answers as (exact) rational numbers.

a The midpoint estimate, over the interval

b) The midpoint estimate, over the interval

c) The midpoint estimate, over the interval

d) The midpoint estimate, over the interval

e)  What do these estimates suggest about the area over the interval and the area over the interval

Answer 1

a) The width of the area element is x_U - x_L or 7-1 = 6

the height is taken to be the function value at the midpoint: f(1/2 (x_U + x_L)) = 1/(4) = .25

The estimate of the are is height*width = 6*.25 = 1.5 (actual 1.95)

b) You can do.

c and d are repeats as listed. I assume that you had to subdivide the interval some number of times.

If you have a bunch of intervals, you do the same thing for each interval and add them up.