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 whi

Question

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.

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Ivy 4 weeks 2021-09-19T04:13:08+00:00 1 Answer 0

Answers ( )

  1. Emma
    0
    2021-09-19T04:15:00+00:00

    The region R is the set of points

    R=\{(x,y)\mid0\le y\le1,y\le x\le2-y\}

    Then the volume is given by the integral,

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

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