I need to find the work of the vector field
F= 3xi+6y^2j+4zk
along the path
r(t)=ti+cos(t)j+3sin(t)k
from the point (3,0,0) to (pi,0,1).
I know the fundamental theorem of calculus states to take a function differentiable to the vector field, insert the given endpoints, and take the difference.
I'm having trouble finding that function. I know I can take the derivative of r(t) and multiply it with the integral of the field, and though that would be equivalent, I'm having trouble determining how to know that I'm on the right track.
r'(t)=i-sin(t)j+3cos(t)k
I'm stumped as to where to go from here.
F= 3xi+6y^2j+4zk
along the path
r(t)=ti+cos(t)j+3sin(t)k
from the point (3,0,0) to (pi,0,1).
I know the fundamental theorem of calculus states to take a function differentiable to the vector field, insert the given endpoints, and take the difference.
I'm having trouble finding that function. I know I can take the derivative of r(t) and multiply it with the integral of the field, and though that would be equivalent, I'm having trouble determining how to know that I'm on the right track.
r'(t)=i-sin(t)j+3cos(t)k
I'm stumped as to where to go from here.