2. 15.6, Triple Integrals in Rectangular Coordinates:
(a) Sketch the region bounded by the surfaces $z = x^2 + y^2$, $x = 0$, $y = 0$, $z = 0$, $x + y = 1$.
Each pair of the surfaces intersects in a curve. Be sure to include these curves in your
sketch. Then use a triple integral to calculate the volume of the solid.
(b) Find the volume of the region in the first octant bounded by the coordinate planes, the
plane $x + z = 2$, and the parabolic cylinder $y = 9 - x^2$.
