We would like to calculate the volume under the surface defined by a continuous function z=f(x,y) which is defined on a closed rectangle R=[a, b]x[c,d]. We will use Riemann sums for this purpose.
1. Choose a continuous real valued function which is defined for all (x,y) for which the exact area can be found by definite integral (Note: x and y are also real numbers)
2. Write the detailed algorithm for estimating the volume in question.
3. Write the code in Java or C++ that estimates the volume according to the algorithm provided.
a) Calculate the exact volume of the function by definite integral
b) Calculate estimated volume of the function by using your program
c) Calculate the relative error of the estimated volume with respect to the exact volume.
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