Chapter 5.4, Problem 234E

[T]

a. Apply the midpoint rule to approximate

${\displaystyle \underset{B}{\iiint }{e}^{-x^2}dv}$over the solid

$B=\left\{\left(x,y,z\right)|0\le x\le 1,0\le y\le 1,0\le z\le 1\right\}$ by using a partition of eight cubes of equal size. Round your answer to three decimal places.

b. Use a CAS to improve the above integral approximation in the case of a partition of n³cubes of equal size, where n = . 3,4..... 10.