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Math Help - line integral example

  1. #1
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    line integral example

    Could some offer an example of finding the line integral of a circle’s arc which is not centered at the origin and which passes through a simple 2-plane vector field?

    I am having trouble parameterizing a circle’s path into terms of sine and cosine.

    Thanks in advance.
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  2. #2
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    Re: line integral example

    Hey Kvandesterren.

    Is this 2-plane vector field just an arbitrary plane embedded in R^3?
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  3. #3
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    Re: line integral example

    yes
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  4. #4
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    Re: line integral example

    Can you rotate the plane to get it axis aligned with the x-y plane and then carry out the line integral (via a linear transformation)?

    Are you aware of the substitution theorem for integrals in multiple dimensions?
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  5. #5
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    Re: line integral example

    I don't believe you are asking about a general plane in 3 dimensions. I interpret your question as just about integrating u(x,y)i+ v(x, y)j about an arbitrary circle, or arc of a circle, with center at some point other than (0, 0). That's much easier!

    A circle, with radius R, with center at (x_0, y_0) is given by (x- x_0)^2+ (y- y_0)^2= R and standard parametric equations x= x_0+ R cos(\theta), y= y_0+ R sin(\theta).
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