I understand that we are finding the area of a curve given by some function f(x) over the area of another curve C. (I've also successfully plugged and chugged my way through my homework, without understanding what I was doing)
These are some of the questions that I am a little fuzzy about:
1. Could I use a line integral in only 2 dimensions? (for example: to find the area between the curves y=x^2 and y=2x from x is in [0,2]? If so, how?)
2. Moving to more dimensions, the formula my book gives me is:
∫cF . Vds =∫ab F(a(t)) . a'(t)dt
Where C is a smooth oriented curve, whose orientation is given by V and F is a continuous vector field. (I understand individually what each of these terms mean, but am having trouble understanding what this formula is finding.
What, geometrically, is this formula finding?