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Line integral of scalar field ( piecewise curve)

  1. Jul 25, 2016 #1
    1. The problem statement, all variables and given/known data

    for the line segment c2 , why did the author want to differentiate dx with respect to dy ? and he gt dx = 0 ?

    I'm curious why did he didnt do so for C3 , where dy= 0 ..Why didnt he also differentiate dy with dx ? dy/dx = 0 ?
    2. Relevant equations


    3. The attempt at a solution
    is there anything wrong with the working ?
     

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  2. jcsd
  3. Jul 26, 2016 #2
    actually one differentiates a function f(x,y) with respect to variable x or y;
    your statement is in error - during c2 he is taking d/dy of f=x and as y is only variable on the path the slope of the path d/dy of x comes to zero.

    here also the author is taking d/dx of the function f=y as the variable is x ...not y as in the previous path and the slope is again zero.
    slope of a curve is defined by tan of the angle made by a drawn tangent at the point under consideration..
    Imagine f equivalent to say F(x,y) .....the graph of f is of a type x=0 for the c2 ( y from 1 to zero) and y=0 for c3 ( x going from 0 to 1)
     
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