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Definite Integral Word Problem

  1. Apr 24, 2009 #1
    1. The problem statement, all variables and given/known data
    A rectangular pool is 10 meters wide and 25 meters long. The depth of water "x" meters from the shallow end of the pool is MSP22607039579497235809_347MSPStore.gif

    Part A. Write a left-hand Riemann Sum with 5 terms that approximates the volume of the water in the pool. Is your approximation an underestimate or an overestimate? Explain.

    Part B. Write a definite integral that gives the exact volume of the water in the pool.


    3. The attempt at a solution
    Don't know where I should even begin. Forgot my book at school and its vacation time:(
     
  2. jcsd
  3. Apr 24, 2009 #2

    HallsofIvy

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    Draw a picture looking at the pool from the side. It should be a quadrilateral with base 25 m long, two right angle ends, and end heights [itex]0^2/175+ 1= 1[/itex] and [itex]25^2/175+ 1= 4.57[/itex] meters (not a very deep pool!). A cross section, of width h at distance x from the shallow end, is 10 by 4.57 by h. Take h= 25/n where n is the number of steps you decide to use.
     
  4. Apr 24, 2009 #3
    i still dont quite understand :(
    Your heights aren't showing up.
     
  5. Apr 24, 2009 #4
    anyone?
     
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