3. Let V be the solid given by {(x, y, z): 0 < 12/<1-12|-y|}.
(a) Draw V. Set up a double integral for the volume of V, SS f(x, y) dx dy, where f(x, y) = z. Evaluate
this integral to find the volume of V.
(b) Find SSS vz2 dx dy dz.
Hints: Label all surfaces and coordinates of interest. You can sketch the volume either by hand or by using
a computational visualisation tool, by including a snapshot of the sketch with all labelling! You must explain
in words what software you used, include a screenshot of your code (just collate it). Think at what is the
right 3D orientation of the (2,y, z) axes to visualize the volume at its best representation. A good view of
the volume will help you with choosing the right limits of integration.
(15 marks]