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Some questions on Green's Theorem.

  1. Apr 16, 2013 #1
    I am working on the derivation of Green's Theorem. I might have more question in later post. I am looking at this pdf file:

    http://www.math.psu.edu/roe/230H/slides_14nov.pdf

    In page 3, ##\int \int_R\frac{\partial N}{\partial x} dx dy=\int_c^d\int_a^{g(y)}\frac{\partial N}{\partial x} dx dy##

    How is ##\int_a^{g(y)}\frac{\partial N}{\partial x} dx \;=\;N[g(y),y]\;-\;N(a,y)## as show in page 3? I don't know the steps to arrive to this.
     
  2. jcsd
  3. Apr 16, 2013 #2

    AlephZero

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    This is just the fundamental theorem of calculus, or the idea that an integral is an "antiderivative".
    $$\int \frac{df(x)}{dx}\,dx =f(x) + C$$
    $$\int_a^b \frac{df(x)}{dx}\,dx =f(b) - f(a)$$
    When you do the "inside" integration over x, y is a constant, so N is just a function of x.
     
  4. Apr 17, 2013 #3
    Thanks, yes I forgot about this. Just went back and studied up.
     
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