Integration of a vector with respect to a vector.

[Ceeerson]

will someone give me an explanation of the process of integration of a vector with respect to another vector. the reason i ask is because in the topic of electricity i am discussing the electric flux of a point charge inside a solid surface. I know that the dot product is related, and i can even see how the limit as the number of subintervals approaches infinity, then Ʃ running from k = 1 to n of the vector f(x*)times the vector(Δx*) times (cosθ ) is equal to the definite integral, it would just take forever to count and and i wouldn't know how to evaluate the integral without knowing the antiderivates, my main concern is integrating from a to b of the electric field dot da, and while on the topic, will someone please explain how area can be a vector please, i know that you can pull out all the constants, but and even the antiderivative of 1/r^2 but i just don't understand the integration and what happens. if that makes sense.

sincerely confused

 

[SteamKing]

You should take a course in vector calculus. What you are asking is usually covered over several weeks of such a course.

 

[Ceeerson]

oh ok well i won't have that option for a while so is there a recommended book for beginners over vector calc, it doesn't have to be dumbed down, just interpret-able any insight would be greatly appreciated!