# Evaluate the line integral given the path of a helix?

Evaluate the line integral

$$\int_C zdx + xdy + xydz$$

where C is the path of the helix r(t) = (4cost)i + (4sint)j + (t)k on $0\le t \le 2\pi$

I solve this problem, but my answer was wrong.

x= 4cost

y= 4sint

z= t

dx= -4sint dt

dy= 4cost dt

dz= dt

I plugged these into the integral above and integrated to get

$$4tcost - 4sint + 4t +sin(4t) + 4sint \ |_0^{2\pi}$$

I solved this and got 16$\pi$ Can someone tell me where I am going wrong?

• The primitive function looks wrong, but without giving more details on how you get there, I can only say it is in the step from simplifying $z\,dx+x\,dy+xy\,dz$ or doing the actual primitive it goes bad. I suggest you provide the details of that calculations if you need further help. – mickep Apr 4 '15 at 19:56

$$\int_0^{2\pi}(16 \cos^2 t+16 \cos t \sin t-4t \sin t)dt=$$ $$= 4\left(2t-\sin t +\sin 2t-2\cos^2 t+t \cos t \right) |_0^{2\pi}= 24 \pi$$