Problem $2(5\_$pts$.)$:

The vertical stress ${}_v$ in a soil at any depth below the surface can be estimated as a function of the soil unit weight $$ by the equation,

${}_v={\displaystyle \underset{0}{\overset{Z}{}}}({}_v)dz={\displaystyle \underset{0}{\overset{100}{}}}(95+0\mathrm{.}0007{}_v)dz$

If a particular stratum has a function $=95+0\mathrm{.}0007{}_v,$ where $$ is in pcf and ${}_v$ is in psf$,$ find the vertical stress at a depth of $100$ feet below the surface.