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!

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


    User Avatar
    Science Advisor

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Definite Integral Word Problem