1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Upper Bounds Integration

  1. Apr 25, 2008 #1
    [SOLVED] Upper Bounds Integration

    1. The problem statement, all variables and given/known data
    Integrate y=4x from 2 to 5 using the limit with circumscribed rectangles.

    2. Relevant equations

    A=lim(n to inf.) Summation of f(xsubi) times delta (xsubi)

    3. The attempt at a solution

    =64/n^2((n^2+3n)/2))= 32lim((n+3)/n)) =32. But from integration the answer is obviously 48. What am I doing wrong? (Sorry about lack of typo skills-newbie)
  2. jcsd
  3. Apr 25, 2008 #2
    why do you think the answer is obviously 48?
    Your answer isn't correct again thout..
  4. Apr 25, 2008 #3
    well i got 42 as my answer, either by directly integrating

    [tex]\int_2^5 4xdx[/tex] and also by using Rieman sums.

    I'll try to post my work, on my next post.
  5. Apr 25, 2008 #4
    Sorry-wrong limits!

    Sorry! The limits were 1 to 5, not 2 to 5!
  6. Apr 25, 2008 #5
    we want to calculate

    [tex]\lim_{n\to\infty}\sum_{i=1}^{n}f(\epsilon_i)\delta x_i[/tex]

    now let us create n mini segments on the segment [2,5]

    that is let the points be


    Now our concern is to determine what our function will be.
    First let's notice certian facts:

    [tex]\delta x_i=x_i-x_i_-_1[/tex] also let [tex]\epsilon_i=x_i[/tex]

    this way we have:

    [tex]\epsilon_i=\delta x_i+x_i_-_1[/tex]

    also: [tex]\delta x_i=\frac{5-2}{n}=\frac{3}{n}[/tex]

    Now, for to determine our function lets try some values for i=1,2,3,...

    [tex]f(x_1)=4\left(\frac{3}{n}+2\right),f(x_2)=4(\frac{6}{n}+2),f(x_3)=4(\frac{9}{n}+2),......, f(x_i)=4(\frac{3i}{n}+2)[/tex]


    Last edited: Apr 25, 2008
  7. Apr 25, 2008 #6
    Well, then do the same thing as i did here, just take into consideration that you have the lower limit 1, in this case. I am not gonna troube to go the same route again, i think you can do it now. If you can't ask again.

  8. Apr 25, 2008 #7
    Well it doesn't change a lot by the way, the difference is that now you'll have

    [tex]\delta x_i=\frac{4}{n}[/tex] and


    and the answer will be 48.
  9. Apr 25, 2008 #8
    Thanks very much for your replies- I'm still stuck expanding the summation- will attempt another query when I have time, and can clarify.
  10. Apr 25, 2008 #9
    Got it- I wasn't adding the 1 to the 4/n. Thanks again for your answer.
  11. Apr 25, 2008 #10
    I tried to post a detailed answer, including how the summation expanded and all that stuff, but after i typed it all, i don't know for some crappy reason it did not show up. Anyways, i'm glad you got it !
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook