Area bounded by y = \(\left| x \right| \) between the limits 0 and 2 is ________.

The area bounded by the parabola y² = 4x bounded by its latus rectum is ________.

Area bounded by y = e^x between the limits 0 to 1 is ________.

For a demand function p, if \(\int \frac{d p}{p}=k \int \frac{d x}{x}\) then k is equal to ________.

If the marginal revenue of a firm is constant, then the demand function 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 ________.

The demand and supply function of a commodity are D(x) = 25 − 2x and S(x) = \(\frac { 10+x }{ 4 } \) then the equilibrium price P₀ is ________.

The demand and supply function of a commodity are P(x) = (x − 5)² and S(x)= x² + x + 3 then the equilibrium quantity x₀ is ________.

The marginal cost function is MC = 100 \(\sqrt x\). find AC given that TC  = 0 when the out put is zero is ________.

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

Area bounded by y = x between the lines y = 1, y = 2 with y = axis is ________.

When x₀ = 2 and P₀ = 12 the producer’s surplus for the supply function P_s = 2x² + 4 is ________.

When x₀ = 5 and p₀ = 3 the consumer’s surplus for the demand function p_d = 28 − x² is ________.

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

For the demand function p(x), the elasticity of demand with respect to price is unity then ________.

The profit of a function p(x) is maximum when ________.

If the marginal revenue MR = 35 + 7x − 3x², then the average revenue AR 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 marginal revenue and marginal cost functions of a company are MR = 30 − 6x and MC = −24 + 3x where x is the product, then the profit function 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 ________.

If MR and MC denotes the marginal revenue and marginal cost functions, then the profit functions is ________.

If the marginal revenue function of a firm is MR = \({ e }^{ \frac { -x }{ 10 } }\), then revenue is ________.

Area bounded by the curve y = \(\frac{1}{x}\) between the limits 1 and 2 is ________.

Area bounded by the curve y = e^−2x between the limits 0 ≤ x ≤ ∞ is ________.

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