MA103 Lab Report 9 - Substituion Rule; Area Between Curves; VolumesName:Student Number:Winter 20201. [1mark]LAB REPORT WAS SUBMITTED TO DROPBOX IN A CLEAR AND READABLE FORMAT.[That is, the uploaded image was not difficult for the IA to read and then grade.]2. [2marks]Use the substitution rule to evaluateZ3t√3t+ 4dt.Letu= 3t+ 4⇒du= 3tln 3dtandduln 3= 3tdt∴Z3t√3t+ 4dt=Z1ln 3√udu=2√uln 3+C=2√3t+ 4ln 3+C3. [4marks] In economics, a population’s Lorenz curveL(x) gives the percentage (as a decimal) of the country’s distribution ofwealth among the lowest earning percentagex(as a decimal between 0 and 1; e.g., 35% meansx= 0.35) of the population.As an example, ifL(0.4) = 0.1,then this means that the lowest earning 40% of households have only 10% of the entireeconomy’s wealth.The liney=xis called the line of equality since this would mean that the lowest earning 100x% ofhouseholds would have 100x% of the economy’s wealth.Consider a country with a Lorenz curve given byL(x) =xex2-1.