Solve Integral (5): Help on Tricky Calculation Needed

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SUMMARY

The discussion centers on calculating a specific integral presented in a homework statement. The integral involves the variable substitution \(\theta=\frac{\rho}{R}\int\sqrt{\frac{R^2-r^2}{r^2-\rho^2}}\frac{dr}{r}\) and results in an expression involving arctangent functions. Participants emphasize the need for clarity in the integral's presentation, as the original document is not freely accessible. The request for a screenshot or a clearer formulation of the integral is crucial for providing assistance.

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  • Understanding of integral calculus, specifically techniques involving substitutions.
  • Familiarity with arctangent functions and their properties.
  • Knowledge of variable substitution in integrals.
  • Ability to interpret mathematical expressions and equations accurately.
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  • Review techniques for solving integrals involving square roots and rational functions.
  • Study the properties and applications of the arctangent function in calculus.
  • Learn about variable substitution methods in integral calculus.
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Homework Statement


Could anyone show me how integral (5) in this document is calculated. I've been trying and trying but nothing good came out.

[tex]\theta=\frac{\rho}{R}\int\sqrt{\frac{R^2-r^2}{r^2-\rho^2}}\frac{dr}{r}=[/tex]
[tex]=\arctan\left(\frac{R}{\rho}\sqrt{\frac{r^2-\rho^2}{R^2-r^2}\right)-\frac{\rho}{R}\arctan\sqrt{\frac{r^2-\rho^2}{R^2-r^2}[/tex]

Thank you in advance.


Homework Equations





The Attempt at a Solution

 
Last edited:
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Hi, the article is not free to view. Please, write the integral yourself, or post a screenshot from the article containing it.
 
Thank you, fixd it.
 

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