EXERCISES

1. I dare you to do this one by hand: Please plot the surface z = x y sqrt(abs(sin(x)+cos(y))) above the region in the x,y-plane bounded by the x-axis, the y-axis and the line x + y = 4, then compute the volume between this surface and this region in the x,y-plane.

   Hint: Notice that you can use a variable in one of the limits to plot above a non-rectangular region. So if f is defined as a function,

     > plot3d( f(x,y), x = 0..1-y, y = 0..1);
   

   yields a plot above the triangular region bounded by the coordinate axes and the line x + y = 1. Also recall that `wrapping' evalf around an expression will force a numerical answer when one is possible.

2. In both of the following text exercises, use Maple to compute the double integrals, and then sketch the region in the x,y-plane over which the integral is defined.
   1. #5, p. 187
   2. #7, p. 187

3. Setup and evaluate a double integral to find the volume of the first octant part of the solid bounded by the cylinders x² + z² = 7 and y² + z² = 7. Also, generate a three-dimensional plot of the surface of the solid, something like this.