Compute Line Integral: (x/y) from (2,4) to (10,100)

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SUMMARY

The discussion focuses on computing the line integral of the function (x/y) along a specified path from the point (2,4) to (10,100). The path consists of a line segment from (2,4) to (5,25) followed by a parabolic arc from (5,25) to (10,100). Participants emphasize the importance of correctly setting up the integral using appropriate parameterizations for both segments and highlight common pitfalls, such as obtaining negative results when the setup is incorrect.

PREREQUISITES
  • Understanding of line integrals in vector calculus
  • Familiarity with parameterization of curves
  • Knowledge of basic calculus, including derivatives and integrals
  • Experience with functions and their graphical representations
NEXT STEPS
  • Study parameterization techniques for line segments and curves
  • Learn about computing line integrals for different types of functions
  • Explore the use of software tools like MATLAB or Python for numerical integration
  • Investigate common errors in line integral calculations and how to avoid them
USEFUL FOR

Students and professionals in mathematics, physics, and engineering who are working on line integrals and need to understand the setup and computation of integrals over specified paths.

balrog1212
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The question is compute the integral over c of (x/y) where c is the line segment from (2,4) to (5, 25) followed by the parabolic arc from (5, 25) to (10, 100)

I tried setting this up in terms of x and then y using the line integral formula but I am got a negative answer which i know can't be right. Can anyone help me set this up?
 
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What do you have for the function, it's derivative, and the integral?
 
There are many different ways to do such a problem. Show us what you did and we may be able to help.
 

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