Given that A= yai+xaj, P1(1,1,-1) and P2(8,2,-1) evaluate integral from P1 to P2 (A.dl) along the curve x=y^3.
Of course you can. But the problem would be more corectly written where .
In this problem, so . That means that and the dot product gives you an integral of a function of y with respect to y.
Finding "the work integral", given a force vector, is a physics problem which is a special application of "integration on a path". And that is what this problem is asking.
If and the path is given by the parametric equations, , , then
or the path integral which, in turn, is the same as