# Parameterization of a path to find work

• Vitani11
In summary: At the endpoint of the first path, x = -1, y = 1At the endpoint of the second path, x = 1, y = -1At the endpoint of the third path, x = 1, y = 1
Vitani11

## Homework Statement

Evaluate the work done by the two-dimensional force F = ( x2, 2xy ) along each of the following three paths joining the origin to the point P = (1, 1) :
The first two are fine
The last path is: the path given parametrically as x = t3, y = t2 with a parameter t

## The Attempt at a Solution

I think you just take x = t3, y = t2 and you plug them into F = ( x2, 2xy ) and then you set up the integral to find work ∫F⋅ds in terms of t. ∫(t6,2t5)⋅(3t2, 2t)dt = ∫(3t8+4t6)dt. Is this correct?

How would you check?

1. what happens when you use the same method/reasoning on the first two paths?
2. how did the work for the first two paths compare with each other? What do you expect for the third one? What do you get?

Vitani11 said:
∫(t6,2t5)⋅(3t2, 2t)dt = ∫(3t8+4t6)dt. Is this correct?
Yes. You don't spell it out, but it looks like you have understood that ##\vec{ds}=(dx, dy)=(\dot x.dt, \dot y.dt)=(\dot x, \dot y).dt##.

Okay. Now that I understand this part - what about the limits of t? In the original it was a function of two variables going up to the point (1,1). Now that I have paramaterized this (if that is the right wording) what would the limits be in t as a single variable? As in how do I go about figuring it out? I integrated from 0 to 1 because intuitively that makes sense but I'm usually wrong.

Vitani11 said:
Okay. Now that I understand this part - what about the limits of t? In the original it was a function of two variables going up to the point (1,1). Now that I have paramaterized this (if that is the right wording) what would the limits be in t as a single variable? As in how do I go about figuring it out? I integrated from 0 to 1 because intuitively that makes sense but I'm usually wrong.
What are the values of the parameter at the path endpoints?

## 1. What is parameterization of a path to find work?

Parameterization of a path refers to the process of defining and setting specific parameters or criteria for finding employment. This can include factors such as location, job industry, salary range, and required skills.

## 2. Why is parameterization important when looking for work?

Parameterization helps individuals narrow down their job search and focus on opportunities that align with their goals and qualifications. It can also save time by filtering out irrelevant job postings.

## 3. How do I determine my parameters for finding work?

To determine your parameters, you should consider your career goals, skills, and personal preferences. It can also be helpful to research the job market in your desired industry and location to understand the current demand and requirements.

## 4. Can I change my parameters during my job search?

Yes, you can adjust your parameters as needed during your job search. It's important to regularly evaluate and update your criteria to ensure you are targeting the most relevant and suitable opportunities.

## 5. Are there any tools or resources available for parameterization of a path to find work?

Yes, there are various job search engines and career websites that allow you to set filters and parameters for your search. Additionally, career counselors and coaches can provide guidance and support in determining your parameters and navigating the job market.

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