AB$2.$ A post $AB$ is tapered uniformly throughout its height $H.$ The cross sections of the post are square, with dimensions $bb$ at the top and $1\mathrm{.}5b1\mathrm{.}5b$ at the base. Derive a formula for the shortening of the post due to the compressive load $P$ acting at the top. Disregard the weight of the post itself. The modulus $E$ is known. Solution hint: write the width as a function of the height and then the area as the width squared. Then use

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{(a+bx{)}^2}=-\frac{1}{b(a+bx)}$