Section 16.2

Tue, 29 Jul 2014 10:06:31 -0500

I'm having trouble remembering how to parametrize a line when given 3 points. In section 16.2, #10, it asks to compute $\int <1/xy,1/(x+y)>\cdot dr$ along the path from (1,1) to (3,1) to (3,6) using straight line segments. I'm really lost on what to do here.

Answer by Justin for Section 16.2

Tue, 29 Jul 2014 11:09:58 -0500

I believe that to solve this problem, you must set up two separate parametrizations and two separate integrals. The first parametrization/integral should be the line segment from (1, 1) to (3, 1) and the second parametrization/integral should be from (3, 1) to (3, 6). To parametrize these lines, you find the differences in $x$ and $y$ between them and use them in your direction vector. Typically $t$ will range from $0$ to $1$ (see [Christina's answer](http://calc3.askbot.com/question/190/line-integrals/?answer=192#post-id-192) for an explanation why). The first line is parametrized by: $$ \vec p_1 (t) = \langle 1, 1 \rangle + \langle 2, 0 \rangle, $$ where $0 \leq t \leq 1$. The second line can be parametrized in a very similar fashion. Then you must add the result of the two definite integrals together to get the total integral. My apologies for the terse answer, I am on my phone right now!

Section 16.3

Section 16.2

Answer by Justin for Section 16.2