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Fundamental theorem of calculus for double integral

  1. Jun 22, 2015 #1
    I was reading about double integral when a doubt came to my mind: how to find the antiderivative of the function f(x,y), like bellow, and compute the fundamental theorem of calculus for double integral?

    Integrale_multiplo_-_parallelepipedo.png
    [tex] \int_{2}^{8} \int_{2}^{6} f(x,y) dx \wedge dy = ?[/tex]

    OBS: It's not an exercise. I know how to compute the integral above, but, I don't know how do it through of the antiderivative and applying the theorema fundamental of calclus, like that [tex] \int_{a}^{b} f(x) dx = \int_{a}^{b} \frac{dF(x)}{dx} dx = F(b) - F(a)[/tex]. I'm not found anything similar to this...
     
    Last edited: Jun 22, 2015
  2. jcsd
  3. Jun 22, 2015 #2
    What you've set up is called an iterative integral. In its current form, you solve it by first solving the inner integral and then making that answer the integrand for the outer integral. So essentially you can turn a double integral into two single integrals.
     
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