Double Integrals? Double the Fun.

Calculus Level 4

Let N=R(x2+y2) dAN = \iint_R (x^2 + y^2)\ dA over the triangle with vertices (0,0),(2,2),(4,0)(0,0), (2,2), (4,0). If N=abN = \frac{a}{b}, where aa and bb are coprime positive integers, what is the value of a+ba+b?

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