To find Volume under Surface

Using MATLAB,calculate the volume of the solid bounded by the surface x=0; y=0; x+y+z=1 and z=0 and visualize the solid.

Answer 1

[DGM]

Rearrange the implicit equation and observe symmetry and intersections to simplify the task.

syms x y
z0 = 0;
z1 = x+y-1;

vol = int(int(abs(z1)/2,x,0,1),y,0,1)

vol = 

hold on; grid on
h1 = fsurf(z0,[0 1 0 1]);
h2 = fsurf(z1,[0 1 0 1]);
set(h1,'facealpha',0.5);
set(h2,'facealpha',1);
view(-26,16)

I'm not going to bother pruning the surfaces or plotting the vertical faces. This should suffice to make the volume understandable. There are also plenty of other examples of plotting piecewise surfaces using standard tools like surf().