1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Please help Struggling with finding the area using upper & lower sums

  1. Nov 9, 2007 #1
    Please help!!! Struggling with finding the area using upper & lower sums!!

    I can't load the picture on here so I will explain it the best I can...
    It is the graph of 1/x and there are 5 subintervals starting at x = 1 and ending at x = 2.
    It says to use upper and lower sums to approximate the area of the region. Their widths are equal.

    So first I have to find the left and right endpoints I think...but I am still not understanding how to figure them out.
    My guess is...
    Left: 5(i-1)/n
    Right 5i/n
     
  2. jcsd
  3. Nov 10, 2007 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Not quite! You have both "n" and "5" in your formula but, if am reading this correctly, n is the number of intervals and i is "stepping" through those intervals: here n= 5. Since y= 1/x is a decreasing function, its highest value on an interval is at the left end of the interval and its lowes value is at the right end. Your region has length 2-1= 1 and dividing it into 5 regions makes each of length 1/5. Because you are given a specific value of n, there should be no "n" in your formula.
     
  4. Nov 10, 2007 #3
    Oh okay so 1/5 is my width, but then what is my height??
     
  5. Nov 11, 2007 #4

    Gib Z

    User Avatar
    Homework Helper

    Well for the upper sums, the rectangles should go over the graph, so the heights the starting value isn't it? For the lower sums, the rectangles have to be below the graph, so its the smaller value.
     
  6. Nov 11, 2007 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I said before, "Since y= 1/x is a decreasing function, its highest value on an interval is at the left end of the interval and its lowest value is at the right end." Evaluate 1/x at the endpoints of the interval. Of course, the right endpoint of one interval is the left endpoint of the next interval so your sums will differ only at the beginning and end.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Please help Struggling with finding the area using upper & lower sums
  1. Lower sum/ upper sum (Replies: 1)

Loading...