Can you clarify this step (charge density and integrals).

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    Density Integrals
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SUMMARY

The discussion clarifies the integration step in Example 23.8 of "Physics for Scientists and Engineers 8E" by Serway and Jewett, specifically the transition from "2r dr" to "d(r^2)". The fundamental formula of derivatives, d(r^2)/dr = 2r, is highlighted as the basis for this transformation. By multiplying both sides by dr, the relationship d(r^2) = 2r dr is established, confirming the integration process used in the example.

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  • Understanding of basic calculus, specifically differentiation and integration.
  • Familiarity with the concept of charge density in physics.
  • Knowledge of the notation and properties of differentials.
  • Access to "Physics for Scientists and Engineers 8E" by Serway and Jewett for reference.
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  • Review the chapter on derivatives in calculus textbooks to reinforce understanding of differentiation.
  • Study the properties of integrals, focusing on substitution techniques.
  • Explore examples of charge density calculations in electromagnetism.
  • Practice problems related to integration involving variable transformations.
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DannyPhysika
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Hi, if you have the book: Physics for Scientists and Engineers 8E, Serway Jewett

On page 675 (Chapter 23), Example 23.8 there is a step taken during the integration I don't understand:

How do you go from "2r dr" in the numerator to d(r^2)? If there is info or link to the property of integrals which explains this, I would appreciate seeing it. Thank you.
 
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hhhmmm...well, what do you get when you take the derivative or r2 ? In other words, what's d(r2)? is it 2rdr?
 
Hi.

d（r^2）/dr = 2r is fundamental formula of derivative.

multiplying dr on both sides,

d（r^2） = 2r dr

Regards
 

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