Math 3298 - Hampton - Lab 7 - Due 11/1

Surface Area

Most surface area problems give rise to integrals which are too difficult to evaluate exactly.  In this lab we will use mathematica to find the answer to such a problem.

Exercise

1.  Compute the surface area of the portion of the graph of z  = 1 + x^2 y^2 which lies above the unit disk x^2 + y^2 ≤ 1. This is the same as question 19, Chapter 16.6 in the textbook, except that you should get the answer to 8 decimal places.  I recommend working in polar coordinates although it is possible to use Cartesian (rectangular) coordinates if you prefer.  The NIntegrate command for numerical integrals is the simplest tool you can use; it is possible to get an answer in terms of known functions by using Integrate.  The correct answer is shown below to 30 decimal places.

Re[N[π HypergeometricPFQ[{-(1/2),(1/3),(1/2)},{1,(4/3)},-1],30]]