b$)$ A concrete column is to be constructed with the profile shown in Figure Q$\mathrm{.}2$b$.$ Use the

following steps to determine the area moment of inertia $I_{yy}$ of this section about the $y-$axis.

Figure Q$\mathrm{.}2$b: Profile of concrete column.

i$.$ Determine the equation for the parabola bounding the column from above on the

diagram, using your assigned values for $L_1$ and $L_2.$ Note, the form of the parabola is

$y=a{x}^2+b,$ where a and $b$ can be positive or negative.

ii$.$ Determine the equation for the parabola bounding the column from below on the

diagram, using your assigned values for $L_1$ and $L_2.$

iii. Recall that this moment of inertia is defined as:

$I_{yy}={\displaystyle \underset{R}{\overset{\phantom{}}{}}}{x}^{2}dA$

Using the geometry of the section, set up a suitable double integral that will allow you

to evaluate this quantity, make sure that you include the correct limit on each integral.

iv$.$ Evaluate your integral to determine $I_{yy}$ for your allocated parameter values.

L$1=149$

L$2=100$