How do i maximize the line integral?

In summary, the conversation discusses the determination of the path taken from point A to point B in a nonconservative vector field in order to maximize the line integral. However, it is mentioned that this may be an undefined problem without constraints on the coordinates and length of the curve. Additionally, the possibility of circling against the flow to maximize the line integral is brought up, which requires knowledge of the Euler-Lagrange equation as it is a "calculus of variations" problem.
  • #1
okkvlt
53
0
suppose i have a nonconservative vector field.
and there is a path going from point A to point B.
How do i determine the path taken from A to B such that the line integral is maximized?
edit: actually after thinkin about it, this might be an undefined problem unless there is some constraint on the x,y,z coordinates.
 
Last edited:
Physics news on Phys.org
  • #2
okkvlt said:
actually after thinkin about it, this might be an undefined problem unless there is some constraint on the x,y,z coordinates.

And on the length of the curve. Suppose a vector field circles the destination counterclockwise. What's to stop you from circling against the flow, round and round...
 
  • #3
That is a "calculus of variations" problem. Do you know about the Euler-Lagrange equation?
 

1. How do I calculate the line integral?

The line integral can be calculated using the formula ∫ab F(x,y) ds, where F(x,y) is the function being integrated, a and b represent the starting and ending points on the curve, and ds is the length element.

2. What is the purpose of maximizing the line integral?

Maximizing the line integral allows you to find the maximum value of a given function along a curve or path. This can be useful in various applications, such as finding the maximum work done by a force along a certain path.

3. What is the difference between a line integral and a regular integral?

A line integral is calculated along a curve or path, while a regular integral is calculated over a specific interval. Line integrals also take into account the direction of the curve, while regular integrals do not.

4. How do I choose the correct path for maximizing the line integral?

The path chosen for maximizing the line integral depends on the given function and the starting and ending points. It is important to choose a path that is continuous and differentiable in the given interval.

5. Can the line integral be negative?

Yes, the line integral can be negative if the function being integrated is negative along the chosen path. This indicates that the work done by the force along the path is negative.

Similar threads

MHB How to prove this corollary in Line Integral using Riemann integral
    • Calculus
Replies
1
Views
1K
I Is My Calculus of Variations Approach Correct?
    • Calculus
Replies
12
Views
1K
I Help with a 3D Line Integral Problem (segmented line)
    • Calculus
Replies
14
Views
2K
I How to Calculate Surface Integral Using Stokes' Theorem?
    • Calculus
Replies
1
Views
2K
Insights An Overview of Complex Differentiation and Integration
    • Calculus
Replies
1
Views
3K
B Explain Integration to me, please
    • Calculus
Replies
5
Views
2K
Insights A Novel Technique of Calculating Unit Hypercube Integrals
    • Calculus
Replies
1
Views
2K
MHB Triple Integrals: Finding Volume of Solid S Bounded by Planes
    • Calculus
Replies
5
Views
1K
I Is a Line Integral Zero if the Vector Field is Not Conservative?
    • Calculus
Replies
24
Views
2K
I Solving Line Integral Limits: Negative Result?
    • Calculus
Replies
1
Views
922

Hot Threads

Recent Insights

Back
Top