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.

The demand and supply curves are given by \({ P }_{ d }=\frac { 16 }{ x+4 } \) and \(P_s=\frac { x }{ 2 } \) . Find the Consumer's surplus and producer's surplus at the market equilibrium price.

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.

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

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

The marginal cost function of a commodity in a firm is 2 + e^3x where X is the output. Find the total cost and average cost function if the fixed cost is Rs. 500.

Find the area of the region bounded by the curve y = 3 x² - x, X-axis and the lines between x = -1 and x= 1

Find the area of the region bounded by the parabola y² = 4x and the line 2x - y = 4.

Find the area bounded by the curve y = sin x between x = 0 and x = 2π

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

Find the area of the region bounded by the curve y = x²+2, y = x, x = 0 and x = 3.