Double Integrals? Double the Fun.

Calculus Level 4

Let \(N = \iint_R (x^2 + y^2)\ dA\) over the triangle with vertices \((0,0), (2,2), (4,0)\). If \(N = \frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, what is the value of \(a+b\)?

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