Find the mass of the triangular region with vertices (0, 0), (2, 0), and (0, 1), with density function p( x, y ) = x^2 + y^2.

Im having trouble setting up this integral. This is what i came up with:
2 -.5x+1
S S (x^2 + y^2) dydx
0 0

Not sure if that's right tho, It would prob be better to use polar coordinates so i would be integrating:
2pi ?
S S (r^2)rdrd(theta)
0 0

Im just not sure if the bounds are right.

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  1. I think it is easier to proceed with the dx dy integration that you wrote first. I got the same answer. I did not go as far as to evalauate it, however.

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