Find the area of the region bounded by the parabola \(y=4{ - }x^{ 2 }\) , x −axis and the lines x = 0, x = 2.

If the marginal revenue function for a commodity is MR = 9 − 4x². Find the demand function.

The marginal cost function of a commodity is given by MC = \(\frac { 14000 }{ \sqrt { 7x+4 } } \) and the fixed cost is Rs. 18,000. Find the total cost and average cost.

Calculate consumer’s surplus if the demand function p = 122 − 5x − 2x² and x = 6

For the marginal revenue function MR = 6 − 3x² − x³, Find the revenue function and demand function.

Find the area of the region bounded by the parabola x² = 4y, y = 2, y = 4 and the y-axis.

Find the area under the curve y = 4x² - 8x + 6 bounded by the Y-axis, X-axis and the ordinate at x = 2.

Find the area under the curve y = 4x - x² included between x = 0, x = 3 and the X-axis.

The marginal cost function of manufacturing x units of a commodity is 3x² - 2x + 8. If there is no fixed cost, find the total cost function?

If the marginal revenue for a commodity is MR = 9 - 6x² + 2x, find the total revenue function.

The marginal cost at a production level of x units is given by C '(x) = 85 +\(\frac{375}{x^2}\). Find the cost of producing 10 in elemental units after 15 units have been produced?

The marginal cost function is MC = \(\frac{100}{x}\). Find the cost function C(x) if C(16) = 100.

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