How to Correctly Use Substitution for Polar Coordinates in Integrals?

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SUMMARY

The forum discussion centers on the correct application of substitution for polar coordinates in integrals, specifically addressing the confusion around an extra cos²(θ) term. The user initially misapplied the substitution and later realized the necessity of using the Jacobian matrix for accurate transformation. This correction is crucial for properly evaluating integrals in polar coordinates.

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  • Understanding of polar coordinates in calculus
  • Familiarity with integral calculus
  • Knowledge of the Jacobian matrix and its application in coordinate transformations
  • Basic trigonometric identities, particularly involving cos(θ)
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  • Study the application of the Jacobian matrix in coordinate transformations
  • Learn about polar coordinate integration techniques
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Students and educators in calculus, mathematicians focusing on integration techniques, and anyone seeking to deepen their understanding of polar coordinates in mathematical analysis.

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The Attempt at a Solution


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i get an extra cos² thi term! WHY!
am i doing the substitution completely wrong?? or i forgot/left something out which i can not seem to see!

Thank you
 
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4th line, [itex]dw_1= -w\sin \phi d\phi[/itex] unfortunately :(
 
oops, i meant to write dw1 = cos thi dw.
nevermind, i got it.
I have to use Jacobian matrix instead of what i did.
 
Last edited:

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