- #1

PeteyCoco

- 38

- 1

## Homework Statement

Compute the line integral of

[itex]\vec{v} = (rcos^{2}\theta)\widehat{r} - (rcos\theta sin\theta)\widehat{\theta} + 3r\widehat{\phi}[/itex]

over the line from (0,1,0) to (0,1,2) (in Cartesian coordinates)

## The Attempt at a Solution

Well, I expressed the path as a parametrized vector

[itex]\vec{r}(t) = \frac{1}{sint} \widehat{r} + t\widehat{\theta} + \frac{\pi}{2} [/itex], t:(arctan(1/2), pi/2)

the derivative of which is

[itex]\vec{r}'(t) = -\frac{cost}{sin^{2}t} \widehat{r} + \widehat{\theta}[/itex]

I'm looking for the integral to be equal to 2, but whenever I work it out I get a mess of logarithms and square roots. Have I parameterized this the wrong way?