40.4k views
5 votes
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.

User Srsajid
by
9.2k points

1 Answer

2 votes

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

User Chris Laskey
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories