How Do You Calculate a 3D Line Integral Along Multiple Paths?

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SUMMARY

The discussion focuses on calculating a 3D line integral of the vector field v = x²âx + 2yzây + y²âz from the origin to the point (1,1,1) along three different paths. The user specifically seeks guidance on determining the limits for the 3D case, referencing the 2D example provided in "Introduction to Electrodynamics" by Griffiths. The first path outlined is (0,0,0)→(1,0,0)→(1,1,0)→(1,1,1), and the user expresses confidence in completing the remaining parts independently.

PREREQUISITES
  • Understanding of vector calculus, specifically line integrals in three dimensions.
  • Familiarity with the notation and concepts in "Introduction to Electrodynamics" by Griffiths.
  • Basic knowledge of parametric equations for defining paths in 3D space.
  • Proficiency in evaluating limits in multivariable calculus.
NEXT STEPS
  • Study the calculation of line integrals in 3D vector fields using specific examples.
  • Review the concept of parametric equations and how they apply to path integrals.
  • Explore the differences between 2D and 3D line integrals in vector calculus.
  • Practice solving line integrals along various paths to solidify understanding.
USEFUL FOR

Students and professionals in mathematics, physics, and engineering who are working on vector calculus and line integrals, particularly those seeking to deepen their understanding of 3D integrals.

extreme2000
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Dear Users
Please help me in starting this problem I have tried my best but all in vain
Calculate line integral v=X^2{x(Cap)}+2yz{y(Cap)}+y^2{z(Cap)} from origion to point
(1,1,1) by three different routes
(a) (0,0,0)→(1,0,0)→(1,1,0)→(1,1,1)
Now there are three parts in this problem.I want help in what will I consider the limit in 3D case because in example of the line integral of the book (Introducation to Electrodynamics by Griffiths) there is 2D example solved so I want a little help about this part I will do the other 2 parts myself but need help in first part
Thanks
 
Physics news on Phys.org
Does v look like -
[tex]v\,=\,x^2\,\hat{x}+2yz\,\hat{y}+y^2\,\hat{z}[/tex]?
 

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