Question

Find the line integral ,integral F.dr, where F = ( x+y)I+(y-z)j+z*2k,r(t)= t*2 I +t*3 j+t*2k

Answer 1

F•dr = (x+y)(2t) + (y-z)(3t^2) + z^2(2t) dt
= (t^2+t^3)(2t) + (t^3-t^2)(3t^2) + (t^4)(2t) dt
Now just integrate that.