Line integral and parametrization

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SUMMARY

The discussion revolves around the evaluation of the line integral \(\int_{C} 2xyz \, dx + x^2 z \, dy + x^2 y \, dz\) along the curve \(C\) connecting the points (1, 1, 1) and (1, 2, 4). The user has parametrized the curve as (1, 1+t, 1+3t) but struggles with determining the correct limits for the parameter \(t\). The correct answer to the integral is confirmed to be 7, as stated in the reference book.

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  • Understanding of line integrals in vector calculus
  • Familiarity with parametrization of curves
  • Knowledge of evaluating integrals with respect to multiple variables
  • Basic proficiency in calculus, particularly with respect to differential forms
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  • Review the concept of line integrals in vector calculus
  • Study the process of parametrizing curves in three-dimensional space
  • Learn how to determine limits for parameters in line integrals
  • Practice evaluating similar line integrals using different parametrizations
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Students and professionals in mathematics, particularly those studying calculus and vector analysis, as well as educators looking to clarify concepts related to line integrals and parametrization.

Tony11235
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I know this is dumb question but for some reason I have not been able to get the right answer to the following problem:

[tex]\int_{c} 2xyzdx+x^2 zdy+x^2 ydz[/tex]

where C is a curve connecting (1, 1, 1) to (1, 2, 4).

My parametrization is (1, 1+t, 1+3t). My limits are the problem...I think. By the way the correct in answer in the book is 7.
 
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Tony11235 said:
I know this is dumb question but for some reason I have not been able to get the right answer to the following problem:

[tex]\int_{c} 2xyzdx+x^2 zdy+x^2 ydz[/tex]

where C is a curve connecting (1, 1, 1) to (1, 2, 4).

My parametrization is (1, 1+t, 1+3t). My limits are the problem...I think. By the way the correct in answer in the book is 7.

Your parametrization is fine. You said your limits are the problem, but which are you using? Which value t would give your first point? The second?

Alex
 
OMG...I am retarted. :bugeye:
 

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