Question

F(x,y)=xi+yj
∫[0,1,r(t),tcos(7πt) i+tsin(7πt)j]
1.)Plot the path C
2.)Compute the work done W

Answer 1

Ok. So the path is a linear spiral that does 3 and a half full rotations about the origin, ending at (-1,0).

Answer 2

\[\int_C \mathbf{F}\cdot\text{d}\mathbf{r}=\]\[\int_0^1 (t\cos (7\pi t)\mathbf{i}+t\sin (7\pi t)\mathbf{j})\cdot ((\cos (7\pi t)-t\sin (7\pi t))\mathbf{i}+(\sin (7\pi t)+t\cos (7\pi t))\mathbf{j})\,\text{d}t\]Does that make sense?

Answer 3

Now, after a little working out, you should get that to be:\[\int_0^1 t~\text{d}t=\frac{1}{2}\]Make sure to show work! I have skipped a lot of steps.

Answer 4

ya that is good enough i will work out the skipped steps on my own
i appreaciate your great help

Answer 5

you're welcome.