Integrating Over an Oval: Solving Double Integrals with Non-Circular Boundaries

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SUMMARY

The discussion focuses on solving double integrals over non-circular boundaries, specifically the equation Z^2 = 4x^2 + y^2 with the plane z = 1. Participants express confusion regarding the integration limits in polar coordinates due to the oval shape of the boundary. The conversation also touches on the application of Stokes' theorem for finding line integrals related to the given equation. Ultimately, the need for proper limits and coordinate transformations is emphasized for accurate integration.

PREREQUISITES
  • Understanding of double integrals in multivariable calculus
  • Familiarity with polar coordinates and their application
  • Knowledge of Stokes' theorem and line integrals
  • Basic skills in solving equations of conic sections
NEXT STEPS
  • Research the application of polar coordinates to elliptical integrals
  • Study the use of Stokes' theorem in vector calculus
  • Learn techniques for transforming coordinates in double integrals
  • Explore examples of integrating over non-standard shapes in multivariable calculus
USEFUL FOR

Students and educators in multivariable calculus, mathematicians interested in advanced integration techniques, and anyone seeking to understand the application of Stokes' theorem in solving complex integrals.

rad0786
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Anybody know how to integrate over...

Z^2 = 4x^2 + y^2 with the plane z = 1 ?

this comes from my class notes... hmmm.. the proff did some thing really messy... or at least i wrote it messy...

but i got

0(integral)2pi 0(integral)1 z dz d(pheta)

which doesn't seem to make sense since its an Oval, not a circle.

what would be the limits in polar coords?
 
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I'm not sure what you're trying to do.

Are you trying to find the area of the curve

[tex]4x^2 + y^2 = 1[/tex]?
 
yes.. i suppose its that... but the double integral.
infact, the question asks to find the line integral using stokes therm.

so... just how do you doulbe integrate that equation above? its an oval, so you cannot really use polar coords right?
 

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