1. Find the area under the curve below from x = 1 to x = 4. y = 2x + (2/x²) 2. Find the area between the two curves on [2,6] , y = e^{x and} y = (1/x)

3. A fight promoter sells x tickets and has a marginal-revenue function given by the following.R '(x) = 250x - 490Find the total revenue generated form the sale of ticket 1001 through ticket 1300. (That is, integrate from x = 1000 to x = 1300.) Give your answer correct to the nearest dollar.

4. Find the equilibrium for the given supply and demand functions below. s(x) = x²d , (x) = (x - 3)²

5. Consider the following supply and demand functions, where price is expressed as a function of quantity.S(x) = 2x + 5 D(x) = -3x + 13

(a) Find the equilibrium quantity, x_E. (b) Find the equilibrium price, p_E. (c) Find the consumer's surplus at the equilibrium point. (d) Find the producer's surplus at the equilibrium point.