The bar's cross$-$sectional area is given as a function of the axial coordinate $x$ in inches by

$+0\mathrm{.}1x$ in ${?}^2.$ The modulus of elasticity of the material is $E=12E6.$ If the bar is subjected to

tensile axial loads $P=20$ kip at its ends, $(1)$ what is the normal stress at $x=6$ in$?(2)$ what is its

change in length? Hint: ${\displaystyle \underset{0}{\overset{10}{}}}\frac{dx}{1+0\mathrm{.}1x}=\frac{1}{0\mathrm{.}1}ln(1+0\mathrm{.}1x){|}_0^{10}=\frac{ln(2)-ln(1)}{0\mathrm{.}1}=6\mathrm{.}931.$