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Let A = (0, 0), B = (2, 0), and C = (1, 1). Let R be the triangular region in the xy-plane with sides AB, BC, and AC. Set up an integral which gives the volume under the surface f(x, y) = x + y, over the region R and above the xy-plane.

Respuesta :

LammettHash

The region [tex]R[/tex] is the set of points

[tex]R=\{(x,y)\mid0\le y\le1,y\le x\le2-y\}[/tex]

Then the volume is given by the integral,

[tex]\displaystyle\iint_Rf(x,y)\,\mathrm dA=\int_0^1\int_y^{2-y}(x+y)\,\mathrm dx\,\mathrm dy[/tex]