I have a homework question that is as follows:
If $C$ is the curve given by $X ( t ) = ( 1 + 3 \sin(t)) I + ( 1 + 3 \sin^2(t) ) J + ( 1 + 5\sin^3(t) ) K$, $0 ≤ t ≤ π/2$, and $F$ is the radial vector field $F ( x, y, z ) = xI + y J + z K$, compute the work done by $F$ on a particle moving along $C$.
Can someone explain the recipe without actually doing it for me?
I'll respond ASAP.
Thank you!
EDIT:
I'm just kind of stuck because I don't know what $x$, $y$, and $z$ are in terms of $t$. Does $x = 1 + 3\sin(t)$?
EDIT 2:
If $x = 1 + 3\sin(t), y = 1 + 3\sin^2(t), z = 1+5\sin^3(t)$
Then $dx = 3\cos(t), dy = 3\sin(2t), dz = 15\sin^2(t)\cos(t)$