Calculus Volume Word Problem

  • #1

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 [Broken]

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 [Broken]

I'm not sure if I interpreted the question the right way. Any explanations/help would be greatly appreciated. :)
 
Last edited by a moderator:

Answers and Replies

  • #2
22,095
3,285
Yes, I think this is the correct way of doing it.
 
  • #3
Well, that's good to hear. Any additional input? :)
 
  • #4
22,095
3,285
Well, if you've seen multiple integrals. Then maybe you can also try to solve it with them. That would be a nice exercise :smile:
 
  • #5
Thanks, any additional input from anyone?
 

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