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Finding area bounded Supposedly easy yet I have no clue

  1. Apr 15, 2010 #1
    1. The problem statement, all variables and given/known data
    Use the left endpoint graph with the given number of
    rectangles to approximate the area bounded by the
    curve f (x), the x-axis, and the line x = 4.
    f(x)=x2+x

    2. Relevant equations
    No idea.


    3. The attempt at a solution
    Once again, not a clue how to start this.
     

    Attached Files:

  2. jcsd
  3. Apr 15, 2010 #2
    Well, you are calculating the area of each rectangle, and then adding the areas up. You are using 4 rectangles from (0,4). So, you know the length of each rectangle. How do you find the height? Look at where the rectangles touch the graph (i.e., the left endpoint of the rectangle).
     
  4. Apr 15, 2010 #3
    Okay, I kind of guessed my way through it based on my notes and came up with 88/3 or 29.3333_ . Now, the next question asks me to do the same thing, but use the right endpoint graph. Wouldn't the answers be the same?
     
  5. Apr 15, 2010 #4
    You are splitting up the interval (0,4) like this:

    (0, 1) (1, 2) (2, 3) (3, 4).

    Do you see which are the left and right endpoints?
     
  6. Apr 15, 2010 #5
    What did you do to calculate this? I came up with a different answer.
     
  7. Apr 15, 2010 #6
    So for the left endpoints I just do A=b*h and then add them all up?

    Same for the right?
     
  8. Apr 15, 2010 #7
    Yep, that's really all there is to a problem of this type. You want to split up the interval, calculate the height at whichever point you're using (left, right, mid), calculate the area of each rectangle, and sum them up.

    This all leads in to how to calculate the REAL area under the curve, which basically has to do with splitting the interval into infinitely many rectangles!
     
  9. Apr 15, 2010 #8
    Yeah that's what I'm doing now. That part's okay. Just a little long.
     
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