VECTOR INTEGRAL CALCULUS
Piecewise smooth curve example
To get familiar with calculating line integrals of piecewise smooth curves, we shall look at a simple example.
To get familiar with calculating line integrals of piecewise smooth curves, we shall look at a simple example.
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PIECEWISE SMOOTH CURVE EXAMPLE
May want to check out:
LINE INTEGRAL OF A PIECEWISE SMOOTH CURVE
INTERPRETATION OF THE LINE INTEGRAL
Similar to:
VECTOR INTEGRAL CALCULUS >
PIECEWISE SMOOTH CURVE EXAMPLE
May want to check out:
LINE INTEGRAL OF A PIECEWISE SMOOTH CURVE
INTERPRETATION OF THE LINE INTEGRAL
Similar to:
VIDEO LECTURE
MAIN CONCEPTS
The first step is to break up piecewise smooth curve C into smooth curves. Next is to integrate the individual smooth curves independently. Get the Printer Friendly Version COMMENTS
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CONCEPT
Let C be the curve traversing a quarter circle
 from  to  in the plane, then moving along the horizontal line from  to  . We will work with a vector field  . Our objective is thus to find  .
We limit our analysis to a plane because the vector field In this situation, we need to split the piecewise smooth curve C into two separate curves
bearing in mind that the interval in which the parameter varies is as equally important as the x, y functions. We now evaluate the position vector is
and so
and
We now do the same for the other curve
All information presentated, less questions and exercises, is original content of Donny, with slight references to various books.
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is independent of z and has zero k-component and C happens to be on a plane too.
. We shall parameterize these individually as
and 
independently. For 
,
and 
,
. The position vector is 
and 
and so 
.
.
