Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is ________.

The demand and supply functions are given by D(x)= 16 − x² and S(x) = 2x² + 4 are under perfect competition, then the equilibrium price x is ________.

The given demand and supply function are given by D(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is ________.

The demand function for the marginal function MR = 100 − 9x² is ________.

The producer’s surplus when the supply function for a commodity is P = 3 + x and x₀ = 3 is ________.

If MR and MC denote the marginal revenue and marginal cost and MR − MC = 36x − 3x² − 81 , then the maximum profit at x is equal to ________.

Calculate the area bounded by the parabola y² = 4ax and its latus rectum.

Using integration, find the area of the region bounded by the line y −1 = x, the x axis and the ordinates x = –2, x = 3.

An account fetches interest at the rate of 5% per annum compounded continuously An individual deposits Rs. 1,000 each year in his account. How much will be in the account after 5 years.(e^0.25 = 1.284)

Determine the cost of producing 200 air conditioners if the marginal cost (is per unit) is C' (x) = \(\frac { { x }^{ 2 } }{ 200 } \) + 4

If the marginal revenue function is R'(x) = 1500 − 4x − 3x². Find the revenue function and average revenue function.

If MR = 20 − 5x + 3x², find total revenue function.

The demand function for a commodity is p = e^−x. Find the consumer’s surplus when p = 0.5.

A manufacture’s marginal revenue function is given by MR = 275 − x − 0.3x². Find the increase in the manufactures total revenue if the production is increased from 10 to 20 units.

The marginal cost of production of a firm is given by C'(x) = 20 + \(\frac { x }{ 20 } \) the marginal revenue is given by R'(x) = 30 and the fixed cost is Rs. 100. Find the profit function

The price elasticity of demand for a commodity is \(\frac { p }{ { x }^{ 3 } } \). Find the demand function if the quantity of demand is 3, when the price is Rs. 2

Find the area bounded by y = 4x + 3 with x- axis between the lines x = 1 and x = 4

The demand function of a commodity is y = 36 − x². Find the consumer’s surplus for y₀ = 11

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 marginal cost function of manufacturing x shoes is 6 +10x − 6x². The cost producing a pair of shoes is Rs. 12. Find the total and average cost function.

The marginal cost and marginal revenue with respect to commodity of a firm are given by C'(x) = 8 + 6x and R'(x)= 24. Find the total Profit given that the total cost at zero output is zero.