6) Calculate the area under the graph of the function f(x ) = 3x + 2x-1 between X= D and X = 1. Draw the graph and show the area in question . ( indicate the max / min points, inter- cepots, and shade the area ) 7) An oil company considers which technology to use over the next 10 years. The quantities of oil ( barrels per year ) for each technology are given by f (t ) = lotz t' and q (t) = 13 - zot? + loot, where t is time in years ( t Elo, 10]) a/ Draw the two functions, f and g on the same graph ( show max, min, and intercepts. Show your work) 4 ) Show that the total quantity yielded by the g tech- nology is greater than the one yielded by the f technology at any time ( S"gde > So fat ). 8 ) Suppose that the inverse demand and supply curves for a commodity are given by P = f(9) = 600/19+5) andp = g (9 ) = 2+2 Find the equilibrium price and quarility and calculate the consumer surplus. 9 ) Calculate the following integrals using the change of Variable ( substitution) method: 9 a ) S( x + 5 ) ? d x 961 3 x +2 dx X' + 2x -1 e 9 0 ) lux dx qd) K x X X - 3 4 10) Consider the integral Ex F ( x ) = ) txt. Calculate df for X= 1. dx