Calculating the Total Mass on a Surface Bounded by a Triangle

[r-rogerthat]

Homework Statement

Let the surface S be the part of the plane 2x-y+z=3 that lies above the triangle in the xy plane that is bounded by the lines y=0, x=1 and y=x. Find the total mass of S if its density (mass per unit area) is given by

ρ(x,y,z)= xy+z

Homework Equations

The Attempt at a Solution

Ok so i know this is a double integral. the limite will be
0≤x≤1
0≤y≤2x-3

and f'(x)= 2, f'(y)= -1

√(f'(x) + f'(y) + 1)= √6

so my equation is

√6∫∫(xy+z)

and i have a feeling I am meant to convert this into polar coordinates but how do you convert the limits to polar coordinates?

 

[voko]

You don't need any polar coordinates here. You simply need to express z via x and y in the integral you have got so far. And by the way, it is a mistake not to write dxdy in the integral.

 

[Millennial]

A volume integral seems to yield an easy result here.

 

[r-rogerthat]

thanks heaps guys, i figured it out, and sorry about the late reply