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 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 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 area unded by the curves y = 2^x, x = 0 and x = 2 is________sq.units.

The area of the region bounded by the line 2y = -x + 8, X - axis and the lines x = 2 and x = 4 is ________ sq.units.

The area enclosed by the curve y = cos²x in [0,\(\pi\)] the lines x=0, x = \(\pi\) and the X-axis is ________sq.units.

The area of the region bounded by the line y = 3x + 2, the X-axis and the ordinates x = - 1 and x = 1is_________ sq. units.

The area of the region bounded by the curve y² = 2y - x and the y-axis _____ sq. units

The area bounded by the curve y = 4ax and the lines y² = 2a and Y-axis is _______ sq. units.

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

Find the area of the region lying in the first quadrant bounded by the region y = 4x², x = 0, y = 0 and y = 4

Find the demand function for which the elasticity of demand is 1

Find the consumer's surplus for the demand function p = 25 - x -x² when P_o = 19

Find the producer's surplus for the supply function p = x² + x + 3 when x_o = 4

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

Find the producer’s surplus defined by the supply curve g(x) = 4x + 8 when x_o= 5.

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 marginal revenue function is given by \(R'(x)=\frac { 3 }{ { x }^{ 2 } } -\frac { 2 }{ x } \). Find the revenue function and demand function if R(1) = 6

The price of a machine is 6,40,000 if the rate of cost saving is represented by the function f(t) = 20,000 t. Find out the number of years required to recoup the cost of the function.

Sketch the graph of y = |x - 5|. Evaluate \(\int _{ 0 }^{ 1 }{ |4x-5|dx } \)