Calculus - Hard Volume Problem :\

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SUMMARY

The discussion centers on calculating the volume of water in a rectangular pool measuring 10 meters wide and 25 meters long, with a depth function defined as 1 + (x^2)/175 meters. The integral used to find the volume is established by integrating the depth function over the length of the pool and multiplying by the width. The user confirms the correctness of their approach and seeks reassurance on their solution, which is validated by other forum members.

PREREQUISITES
  • Understanding of definite integrals in calculus
  • Familiarity with volume calculations for three-dimensional shapes
  • Knowledge of functions and their graphical representations
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Study the application of definite integrals in calculating volumes of solids of revolution
  • Learn about the Fundamental Theorem of Calculus and its implications for evaluating integrals
  • Explore advanced integration techniques, such as substitution and integration by parts
  • Practice problems involving volume calculations for various geometric shapes
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Students studying calculus, particularly those focusing on integral applications in volume calculations, as well as educators seeking examples of real-world applications of definite integrals.

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Homework Statement


A pool in the shape of a rectangle is ten (10) m wide and twenty five (25) m long. The depth of the pool water x meters from the shallow part/end of the pool is 1 + (x^2)/175 meters.

Write a definite integral that yields the volume of water in the rectangular pool exactly. And then evaluate this integral.

2. The attempt at a solution

So, to find one section's volume I take the following integral: [PLAIN]http://img801.imageshack.us/img801/5991/calc1.png

So, that gives me one of the 25 foot long section's volumes. Thus, I multiply that integral by ten to yield the following: [PLAIN]http://img80.imageshack.us/img80/1236/calc2.png

I'm not sure if I interpreted the question the right way. Any explanations/help would be greatly appreciated. :)
 
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Looks fine to me.
 
Didn't you already ask 2 days ago? It was fine by then, and it remains fine now :smile:
 
Haha okay thanks. Yeah, sorry micromass, I just wanted to get a little more input as I severely doubted I would have gotten it on my first try. :p

Thanks a bunch guys. :)
 

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