I am trying to understand volume and surface integrals. I do get the idea of the process (find a parametric equation of the volume/surface, integrate afterwards). But I just cannot make up parametric equations on my own.
As an example, one of my tasks is to find the volume of a space limited by the surfaces
$$x=0, y=0, y=6, z=x^2, z=4$$
I pictured it and know what it looks like, but i just cannot think of any real basic approach to find the parametric equation. The 'general volume equation' we learned at uni looks like this:
$$r(u,v,w)=x(u,v,w)\mathbf{e}_1+y(u,v,w)\mathbf{e}_2+z(u,v,w)\mathbf{e}_3$$
where $\mathbf{e}_1,\mathbf{e}_2,\mathbf{e}_3$ are the unit vectors.
Does anybody have a hint or an idea to help me? Thank you in advance!
