Chapter 16.3, Problem 43E

To determine

To calculate: Using the CAS, the Riemann sum approximation $S_{N,N,N}=\frac{1}{N^3}{\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^N{\displaystyle \sum _{k=1}^{N}f(\frac{i}{N},}}}\frac{j}{N},\frac{k}{N})$ for $f(x,y,z)=e^{x^2-y-z}$ for $N=10,20,and30$, the value of I= ${\displaystyle \underset{0}{\overset{1}{\int }}{\displaystyle \underset{0}{\overset{1}{\int }}{\displaystyle \underset{0}{\overset{1}{\int }}f(x,y,z)}}}dV$ and the value of N such that $S_{N,N,N}$approximates I to two decimal places.