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Area approximation and (riemann?) sums

  1. Jan 30, 2009 #1
    1. The problem statement, all variables and given/known data
    I am a first-year physics student learning calculus. my question is about the approximation of the area of a region bounded by y = 0.
    2. Relevant equations
    Use rectangles (four of them) to approximate the area of the region bounded by y = 5/x (already did this one), and y = 0. The height of the tallest rectangle is 5 units, on the y-axis. The numbers(width of the rectangles) on the x-axis are respectively: 1, 2, 3, 4 units.


    3. The attempt at a solution
    The first question was to find the area bounded by y = 5/x which i did: 5/1 + 5/2 +5/3 + 5/4 = approximately 10.4. I know this is correct.
    Then the area bounded by y = 0 would just be zero i assume? is there a certain way to write this one or is it just zero? i cannot see what else it could be.
     
  2. jcsd
  3. Jan 30, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I think they just mean to say find the area bounded BETWEEN the two curves y=5/x and y=0. It's just a single problem, which you already did. Not two separate problems.
     
  4. Jan 30, 2009 #3
    ohhh. good to know. silly me. thankyou
     
  5. Jan 31, 2009 #4

    Mark44

    Staff: Mentor

    science rules,
    You might find it interesting that your estimate of 10.4 for the area bounded by the graph of y = 5/x and the x-axis (the line y = 0) is a very low estimate. In fact, the area of this region is infinite.
     
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