Integrating an inverse square to find U

[Imabioperson]

Hello everyone,

This is probably going to come off as a very silly question. However, I have not had calculus in several years. I was angry that my physics textbook did not have a derivation of Electric Potential Energy. So, I finally came across it, and I see that the integration of the work equation from some point, r_a to another point, r_b yields, kQq (1/r_a - 1/r_b). Can someone explain to me where, (1/r_a - 1/r_b) is coming from?

 

[Doc Al]

Sounds like you realize it's a calculus issue. Review the power rule.

 

[Imabioperson]

So, if you take the anti-derivative FIRST... we yield r^-1 in the numerator. And then, we will take the definite integral, leaving us with (1/upper limit - 1/lower limit)? And then do I switch the sign because of the relation between Work and Potential energy?