Chapter 5.7, Problem 410E

[T] The transformation $T_{k,1,1}:R^3\to R^3,T_{k,1,1}\left(u,v,w\right)=\left(x,y,z\right)$ of the form x = ku, y = v, z = w. where $k\ne 1$ is a positive real number is called a stretch if k >1 and a compression if 0 < k < 1 in the x-direclion. Use a CAS to evaluate the integral ${\displaystyle \underset{s}{\iiint }{e}^{-\left(4x^2+9y^2+25z^2\right)}dxdydz}$on the solid $S=\left\{\left(s,y,z\right)|4x^2+9y^2+25z^2\le 1\right\}$ by considering the compression $T_{2,3,5}\left(u,v,w\right)=\left(x,y,z\right)$defined by $x=\frac{u}{2},y=\frac{v}{3}$ and $z=\frac{w}{5}$ Round your answer to four decimal places.