Find the area contained between the x-axis and one arc of the curve y = cos x bounded between
\(x=-\frac { \pi }{ 2 } and\quad x=\frac { \pi }{ 2 } \)

Find the area under the demand curve xy = 1 bounded by the ordinates x = 3, x = 9 and x-axis

Find the area bounded by one arc of the curve y = sin ax and the x-axis.

Find the area of the region bounded by the line x - y =1, x-axis and the lines x = -2 and x = 0.
x - y = 1

x	0	1
y	-1	0

Determine the cost of producing 3000 units of commodity if the marginal cost in rupees per unit is C'(x) = \(\frac{x}{3000}+2.50\)

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

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

The elasticity of demand with respect to price p for a commodity is \(\frac{x-5}{x}\), x > 5 when demand is x. Find the demand function if prlce is 2, when demand is 7. Also find the revenue function, P

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 total revenuce function, given that when price is 1, the demand is 4.

The marginal revenue function (in thousands of rupees) of a commodity is 7+e^-0.05% where x is the number of units sold. Find the total revenue from sale of 100 units (e^-5 = 0.0067)

The marginal revenue (in thousands of rupees) ot a commodity is R'(x) = 4 + e^-0.03x where denotes the number of units sold. Find the total revenue from the sale of 100 units of the commodity (e' = 0.05)

The marginal cost C'(x) and marginal revenue R'(x) are given by C'(x) = 20 + \(\frac{x}{20}\) and R'(x) = 30. The fixed cost is Rs. 200. Determine the maximum profit.

A Company determines that the -2 2k = k=-1 :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
(i) Total cost function
(ii) Total revenue function
(iii) Profit function

The elasticity of demand with respect to price p is\(\frac{3-x}{x}, x<3\). Find the demand function and  the revenue function when the price is 2 and demand is 1.

The elasticity of demand with respect When to price p for a commodity is \(\frac{p}{x^2}\)demand is x. Find the demand function and revenue function if demand is 2 when price is 3.