Integral Word Problem EXACT PROBLEM Incluced

Click For Summary

Homework Help Overview

The problem involves determining the limits of integration for an integral related to the depth of a pool, modeled by a given function. The pool's length is specified as 25 meters, and the discussion centers on how to set up the integral correctly.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the depth function and the length of the pool, questioning what the appropriate limits of integration should be based on the given dimensions.

Discussion Status

Some participants have confirmed the limits of integration as 0 to 25, while others have provided general guidance on deriving limits from the problem context. The conversation reflects a collaborative effort to clarify the setup of the integral.

Contextual Notes

There is an emphasis on understanding how to derive limits of integration from the problem statement, with some participants expressing uncertainty about their initial thoughts. The discussion highlights the importance of interpreting the problem correctly.

niravana21
Messages
34
Reaction score
0

Homework Statement


Here is the problem:
WordProblem.jpg




The Attempt at a Solution


I can see that as x increases, the deeper the water gets, but I can't figure out my limits of integration.

If somecan just give me the limits, I think I would be all set.
 
Physics news on Phys.org
The depth of the pool is modeled by D(x)=1+x2/175.

According to the problem, the pool is 25 meters long. This is from the shallow end to the deep end.

Knowing that your interval should be as long as the length of the pool, what do you think you should use?
 
Last edited:
The equation for depth involves x, the distance from the shallow end. The pool is 25 meters long. Given this information, what do you think the limits should be?

Edit: Whoops, a little late!
 
0 to 25?
 
Yup.
 
Correct. Generally, whenever you need to integrate something of a fixed length l, your interval should be from 0 to l. This includes when finding area, volume, time, etc, which if you haven't done yet you will. You'll always get your interval from the problem; sometimes you may have to solve for your limits of integration.
 
thanks so much guys. Feel like an idiot.

Feels good to solve a problem.

thanks again. Will definitely post back again.
 
Last edited:

Similar threads

Find volume of this object using integrals
  • · Replies 6 ·
Replies
6
Views
2K
Volume of Static Solid Using Cross-Sectional Area (Integration)
  • · Replies 2 ·
Replies
2
Views
1K
Help please in understanding the limits of this integration
  • · Replies 4 ·
Replies
4
Views
2K
Finding the area of a double integral using dxdy instead of dydx
  • · Replies 4 ·
Replies
4
Views
3K
Evaluate the definite integral in the given problem
  • · Replies 1 ·
Replies
1
Views
2K
Interpret Riemann sum to determine integral
  • · Replies 2 ·
Replies
2
Views
2K
Reversing the order of integration in a double integral
  • · Replies 17 ·
Replies
17
Views
4K
Setting the limits of an integral
  • · Replies 3 ·
Replies
3
Views
2K
Question re: Limits of Integration in Cylindrical Shell Equation
  • · Replies 24 ·
Replies
24
Views
3K
Why no change in limits of integration here?
  • · Replies 7 ·
Replies
7
Views
2K