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

[DannyPhysika]

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.

 

[gsal]

hhhmmm...well, what do you get when you take the derivative or r² ? In other words, what's d(r²)? is it 2rdr?

 

[sweet springs]

Hi.

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

multiplying dr on both sides,

d（r^2） = 2r dr

Regards