VECTOR INTEGRAL CALCULUS
Line Integral example
In order for us to get acquainted with the line integral, let us look at a simple example.
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LINE INTEGRAL EXAMPLE
May want to check out:
DEFINITION OF THE LINE INTEGRAL
LINE INTEGRAL OF A PIECEWISE SMOOTH CURVE
Similar to:
VECTOR INTEGRAL CALCULUS >
LINE INTEGRAL EXAMPLE
May want to check out:
DEFINITION OF THE LINE INTEGRAL
LINE INTEGRAL OF A PIECEWISE SMOOTH CURVE
Similar to:
VIDEO LECTURE
MAIN CONCEPTS
Find  , substitute component functions, integrate w.r.t parameter. Get the Printer Friendly Version COMMENTS
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CONCEPT
Lets evaluate
 where  and C is specified by  and  .
We first need to check whether the position vector is smooth. We have
At this point, the vector field is still defined as x, y, and z. We need to substitute the component functions of On C,
We can now integrate this function w.r.t t in the interval from 0 to 1.
We sum up by saying again to evaluate the line integral, we find the dot product All information presentated, less questions and exercises, is original content of Donny, with slight references to various books.
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which is continuous in the interval so C is smooth. Calculating the dot product gives us
as we are only concern with points on the curve C.
, 
and 
. Substituting into 
gives us
