(Whew)Q1.Find the volume of the prism whose base is the triangle in xy-plane bounded by the x-axis and the lines y=x and x=1 and whose top lies in the plane.

z = f(x,y) = 3 - x - y

Printable View

- Dec 27th 2007, 02:54 AMm777volume of the prism
(Whew)Q1.Find the volume of the prism whose base is the triangle in xy-plane bounded by the x-axis and the lines y=x and x=1 and whose top lies in the plane.

z = f(x,y) = 3 - x - y - Dec 27th 2007, 03:14 AMmr fantastic
$\displaystyle V = \int \int_{R_{xy}} \left[\int_{z=0}^{z=3-x-y} \, dz \right] \, dx \, dy$

where $\displaystyle R_{xy}$ is the region in the xy-plane defined by the projection of the volume V onto the xy-plane.

And you*can*do a double integral over a region in the xy-plane, right?