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Math Help - Average value of f(x,y) = x + y + 2 on the curve C_1

  1. #1
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    Average value of f(x,y) = x + y + 2 on the curve C_1

    Consider C_1 as the curve given by the semicircle of radius two in the upper half plane. Give C_1 the standard orientation (counter clockwise). What is the average value of f(x,y)= x + y + 2 on C_1.

    I'm not even sure where to start. Could I get some help, please?
    Last edited by over9000; February 17th 2014 at 07:47 PM.
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  2. #2
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    Re: Average value of f(x,y) = x + y + 2 on the curve C_1

    why is none of my tex showing?
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  3. #3
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    Re: Average value of f(x,y) = x + y + 2 on the curve C_1

    I think I know what to do magically now that I posted the question. I need to come up with some parametric form for C, so C is x(t) = 2cos(t) and y(t) =2sin(t)> from t=0 to t=pi/4 Now I write everything in terms of the parametrization (that's a word spell checker!) f(x(t), y(t)) = 2cos(t)+ 2sin(t) + 2 and take the integral of that from 0 to 2pi with respect to t. Now I'm not sure what I need to do to get the average of that integral? Divide it by 2pi?
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  4. #4
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    Re: Average value of f(x,y) = x + y + 2 on the curve C_1

    Watch your limits of integration - since its a semicircle, t goes from 0 to pi. And yes, to get the average you divide by the length of the curve, which is 2pi.

    - Hollywood
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  5. #5
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    Re: Average value of f(x,y) = x + y + 2 on the curve C_1

    Thanks Hollywood, you're right. I confused upper half of the plane for the upper right quadrant, so all the work I did needs to be adjusted.
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