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hotcommodity
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[SOLVED] Simple parametrized line integral
This is from an example in my textbook. They want you to evaluate the line integral:
[tex] \int_{C} y dx + 2x dy [/tex]
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, [tex] 0 \leq t \leq 1 [/tex]. 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.
This is from an example in my textbook. They want you to evaluate the line integral:
[tex] \int_{C} y dx + 2x dy [/tex]
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, [tex] 0 \leq t \leq 1 [/tex]. 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.