Integral Word Problem EXACT PROBLEM Incluced

In summary, the problem involves finding the limits of integration for a pool with a depth modeled by D(x)=1+x2/175 and a length of 25 meters. The solution is to use an interval of 0 to 25 meters, which is generally the case for integrating something of a fixed length. The person asking for help thanks the others for their assistance and plans to post again in the future.
  • #1
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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.
 
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  • #2
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?
 
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  • #3
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!
 
  • #5
Yup.
 
  • #6
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.
 
  • #7
thanks so much guys. Feel like an idiot.

Feels good to solve a problem.

thanks again. Will definitely post back again.
 
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1. What is an Integral Word Problem?

An Integral Word Problem is a type of mathematical problem that involves finding the integral of a function over a given interval. It typically involves using algebraic and calculus techniques to solve for the unknown variable.

2. How do I solve an Integral Word Problem?

To solve an Integral Word Problem, you first need to identify the given function and interval. Then, you can use integration rules and techniques such as substitution, u-substitution, or integration by parts to find the antiderivative of the function. Finally, evaluate the antiderivative at the given interval to find the solution.

3. What are the common mistakes to avoid when solving an Integral Word Problem?

Some common mistakes to avoid when solving an Integral Word Problem include forgetting to use the correct integration rule, making errors in algebraic calculations, and forgetting to include the constant of integration. It is important to carefully check your work and make sure all steps are correct.

4. Can I use a calculator to solve an Integral Word Problem?

While you can use a calculator to check your final answer, it is important to show your work and solve the problem manually. This will help you better understand the concept and identify any mistakes you may have made along the way.

5. How can I practice solving Integral Word Problems?

There are many resources available for practicing Integral Word Problems, including textbooks, online tutorials, and practice worksheets. You can also create your own problems by using different functions and intervals to challenge yourself and improve your skills.

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