Is There a Trick to Integrating with Law of Cos?

In summary, The speaker is struggling with integrating for finding electric field or potential in Electrostatic problems. They have tried using basic methods such as u-substitution and integration by parts, but have not been successful. They are now considering using the law of cosines to simplify the denominator. They have provided a picture for reference.
  • #1
cbirk
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I hope I am posting this in the correct area. This is not specificly a homework question, but something that keeps stumping me on numerous Electrostatic problems.

When attempting to Intigrate for finding the electric field or potential, I frequently end up with an integral over the form ∫∫∫ [itex]r^{2}[/itex] / ( [itex]r^{2}[/itex] + [itex]b^{2}[/itex] - 2rb cosθ) dr sinθ dθ dΦ

I was wondering if there is some sort of method the integrate this that I seem to be missing. A basic U sub doesn't work, and I can't get Integration by parts to do anything but make it worse. I have never been very good at remembering the trig tricks to integration so I was really hoping someone could help me out here. I am lost, and this is costing me lots of points on homeworks and tests.

Thanks in advance.
 
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  • #2
Also after being stumped for days, I am pretty sure that the way the law of cosines is layed out... that cosθ is equivelent to Adjasent / Hyp = b/r which would simplify the entire denominator to a simple [itex]r^{2}[/itex] - [itex]b^{2}[/itex]

This look at all correct? I have added a picture so you can see the layout

stuff.jpg
 

1. What is the Law of Cos?

The Law of Cos, also known as the cosine law, is a mathematical formula used to calculate the side length or angle of a triangle. It states that the square of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the two sides and the cosine of the included angle.

2. How is the Law of Cos used in integration?

The Law of Cos is used in integration to calculate the area under the curve of a trigonometric function. By using the cosine law, we can determine the value of the definite integral of a trigonometric function.

3. What are the key steps in integrating with Law of Cos?

The key steps in integrating with Law of Cos include identifying the trigonometric function, using the cosine law to rewrite the function in terms of cosine, applying the integration rules, and solving for the definite integral.

4. What are the common mistakes when integrating with Law of Cos?

One common mistake when integrating with Law of Cos is forgetting to apply the appropriate integration rules, such as the power rule or trigonometric identities. Another mistake is not properly identifying the trigonometric function and using the wrong formula.

5. How can I practice integrating with Law of Cos?

You can practice integrating with Law of Cos by solving various integration problems that involve trigonometric functions. You can also use online resources or textbooks that provide step-by-step examples and practice questions. Additionally, you can seek help from a tutor or attend a study group to improve your understanding and skills in integrating with Law of Cos.

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