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Homework Help: Integration + change of order

  1. Mar 5, 2006 #1
    Consider the integral:
    [tex] \int_R x^2 + y^2 dA [/tex]

    with the two graphs 2x-y = 0 and [tex] x^2 [/tex] - y = 0

    therefore y = [tex] x^2 [/tex] and y = 2x are the two functions
    and the point of intersection is at (0,0) and (2,4)

    [tex] \int { \int x^2 + y^2 dx } dy [/tex]
    (a - is top point of the integral and b - is the bottom)

    therfor the domain for the first integral (dx) is b = y/2 and a = [tex] y^1^/^2 [/tex]

    and for the second integral (dy) is b= 0 and a = 4

    but when i switch the order to """"" dy dx.... i get a different #.

    therefore my new a,b for the integrals are
    for the first integral (dy) b = [tex] x^2 [/tex] a = 2x
    for the second integral (dx) b = 0 a = 2

    is my change of order correct or did i do somthing wrong??
  2. jcsd
  3. Mar 5, 2006 #2
    never mind.. my change of order is correct.. i just messed up on my integration
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