The Volume as a Double Integral

Problem 1

Find the general formula as a double integral in rectangular
coordinates that allows to find the volume between the lines *x*
= *a*, *x* = *b*, the curves

*y* = *g*(*x*), *y* = *f*(*x*),
and the surfaces *z* = 0, *z* = *F*(*x*,
*y*).

Problem 2

Using a double integral in rectangular coordinates, determine
the volume of the solid in the first octant under the surface *z*
=
and beside the plane *x* + 2*y* = 2.