# Definite Integral Word Problem

1. Apr 24, 2009

### niravana21

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

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. Apr 24, 2009

### HallsofIvy

Staff Emeritus
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 $0^2/175+ 1= 1$ and $25^2/175+ 1= 4.57$ 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.

3. Apr 24, 2009

### niravana21

i still dont quite understand :(
Your heights aren't showing up.

4. Apr 24, 2009

### niravana21

anyone?

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