Labware - MA35 Multivariable Calculus - Three Variable Calculus



Total Mass of Regions between Function Graphs


As was true with simple regions, in order to find the total mass of a region between two function graphs, we must integrate the density function times some tiny volume dV over the given region. The difference here is in the limits of integration. x and y will still begin and end at constants. The lower and upper limits of z, however, will be functions of x and y.



  • 1. How can you modify the problem of finding the mass of a region between two function graphs so that you only need to consider one function graph?
  • 2. Find two functions of x, y, and z which enclose a region whose volume is finite (i.e. they intersect to form a closed surface).