asked 2014-07-29 10:06:31 -0600
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.
answered 2014-07-29 11:09:58 -0600
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 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!
Asked: 2014-07-29 10:06:31 -0600
Seen: 15 times
Last updated: Jul 29 '14
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