Find the area of the region bounded by the line y = x - 5, the x-axis and between the ordinates x = 3and x = 7

The Marginal revenue for a commodity is MR=\(\frac { { e }^{ x } }{ 100 } +x+{ x }^{ 2 }\), find the revenue function.

The elasticity of demand with respect to price for a commodity-is a constant and is equal to 2. Find the demand function and hence the total revenue function, given that when the price is 1, the demand is 4.

A company determines that the marginal cost of producing x units is C'(x) = 10.6x. The fixed cost is Rs. 50. The selling price per unit is Rs.5. Find the profit function.

The demand and supply functions under pure competition are P_d = 16 - x² and p_s = 2x² + 4. Find the consumer's surplus and producer's surplus at the market equilibrium price.