Simple parametrized line integral

[hotcommodity]

[SOLVED] Simple parametrized line integral

This is from an example in my textbook. They want you to evaluate the line integral:

\int_{C} y dx + 2x dy

for the straight line segment in the plane from A(1, 1) to B(2, 4).

The example says that this segment can be parametrized as x = 1 + t, and y = 1 +3t, 0 \leq t \leq 1. I don't know as much about parametrization as I should, so I assume I'm missing something simple here. How are they able to set up x(t) and y(t) ?

Also, could someone explain the point of a line integral. My book shows that it can be used to find the mass of a wire given the density function of the wire. Is this all it's used for?

Any help is appreciated.

 

[EnumaElish]

Parametric curves "can be anything." Suppose x represents temperature and y is rainfall throughout the day. At midnight the temperature and the rainfall are both 1. As time passes, each changes with time. At the end of the day, x = 2 and y = 4.

It can be used to measure of the total effect of any vector field along a given curve (path) in that field. See http://en.wikipedia.org/wiki/Line_integral

 

[hotcommodity]

I see, thank you for the response. It just confused me because the book didn't introduce the parametric equations until it stated the solution, which led me to believe that I was supposed to know what those curves were ahead of time.