Solve Integral (5): Help on Tricky Calculation Needed

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In summary, solving an integral involves finding the anti-derivative of a given function using techniques such as integration by parts, substitution, or integration tables. It is important to determine the limits of integration and check the solution by taking the derivative or using online calculators. Solving integrals allows us to find the area under a curve and solve real-world problems in various fields. Tips for solving tricky integrals include breaking them into smaller parts, using symmetry or trigonometric identities, and practicing different techniques. While calculators can be used, it is important to understand the concepts behind solving integrals.
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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

 
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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.
 
  • #3
Thank you, fixd it.
 

1. How do I solve an integral?

Solving an integral involves finding the anti-derivative of a given function. This can be done using various techniques such as integration by parts, substitution, or using integration tables. It is important to first determine the limits of integration and then follow the appropriate method to solve the integral.

2. What is the purpose of solving integrals?

Solving integrals allows us to find the area under a curve and can be used to solve various real-world problems in fields such as physics, economics, and engineering. It also helps in finding the maximum or minimum values of a function and can be used to determine the volume of a solid with known cross-sectional area.

3. How do I know if I have solved an integral correctly?

You can check your answer by taking the derivative of the anti-derivative you found. If the derivative matches the original function, then you have solved the integral correctly. You can also use online integral calculators to verify your answer.

4. What are some tips for solving tricky integrals?

Some tips for solving tricky integrals include breaking the integral into smaller parts, using symmetry or trigonometric identities, and practicing different techniques for solving integrals. It is also important to carefully consider the limits of integration and make sure they are correctly incorporated into the solution.

5. Can I use a calculator to solve integrals?

Yes, there are many online and offline calculators that can solve integrals. However, it is important to understand the concepts and techniques behind solving integrals rather than solely relying on calculators. This will help in solving more complex integrals and understanding the solutions better.

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