Definite Integral Word Problem

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Homework Help Overview

The problem involves calculating the volume of water in a rectangular pool using both a left-hand Riemann sum and a definite integral. The pool dimensions are specified, and the depth of water is described as a function of distance from the shallow end.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to start the problem, indicating a lack of resources. One participant suggests visualizing the pool's cross-section and provides a formula for the heights at each end. Another participant questions the clarity of the height values presented.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of the problem. Some guidance has been offered regarding the visualization of the pool and the formulation of the Riemann sum, but there is no clear consensus or resolution yet.

Contextual Notes

The original poster mentions forgetting their textbook, which may limit their ability to engage with the problem fully. There is also a suggestion of using a specific number of steps for the Riemann sum, indicating a potential constraint in the approach.

niravana21
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Homework Statement


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
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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.

The Attempt at a Solution


Don't know where I should even begin. Forgot my book at school and its vacation time:(
 
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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 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.
 
i still don't quite understand :(
Your heights aren't showing up.
 
anyone?
 

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