Originally Posted by

**affslick** I'm taking a 5-week Calc III summer course, and I'm working on a practice problem in preparation for the exam tomorrow morning. I've been doing fine up until we started on Line Integrals. I've read a number of tutorials, my book, etc., but this one keeps slipping by... Trying various methods, I've gotten the following numeric answers:

On Paper (with the assistance of a TI89): 270.899

Maple (using the VectorCalculus LineInt command): 15.739

Maple (working out each step): 147.927

The problem is as follows: (with some of my likely incorrect work):

Find the work done by the force:

$\displaystyle \vec{F}=(x+y)\vec{i}+(2x-y)\vec{j}$

acting on a body as it moves along the curve between the values:

$\displaystyle t$ between $\displaystyle 0$ and $\displaystyle \pi$

with

$\displaystyle \vec{r}=2t\vec{i}+sin(t)\vec{j}$.

I'm computing:

$\displaystyle x=2t$

$\displaystyle y=sin(t)$

$\displaystyle r'(t)=[2, cos(t)]$

So...

$\displaystyle \vec{F}=(2t+sin(t))\vec{i}+(2(2t)-sin(y))\vec{j}$

$\displaystyle \int_0^\pi \! \vec{F} \cdot \left|\left|r \right|\right| \, dt=\int_0^\pi \! ((2t+sin(t))\vec{i}+(2(2t)-sin(y))\vec{j} \cdot \sqrt{(2t)^2 + (sin(t))^2}) \,dt$

I'll stop there, as my mistake is probably well before this point... If anyone could help me figure this out, with the simplest language possible, it would be greatly appreciated.

Thanks,

Chris