Using integration, find the area of the region bounded by the line y −1 = x, the x axis and the ordinates x = –2, x = 3.

The marginal cost function of manufacturing x shoes is 6 +10x − 6x². The cost producing a pair of shoes is Rs. 12. Find the total and average cost function.

The rate of new product is given by f (x) = 100 − 90 e^−x where x is the number of days the product is on the market. Find the total sale during the first four days. (e^–4 = 0.018)

A company receives a shipment of 200 cars every 30 days. From experience it is known that the inventory on hand is related to the number of days. Since the last shipment, I(x)=200 − 0.2x. Find the daily holding cost for maintaining inventory for 30 days if the daily holding cost is Rs. 3.5

The marginal cost function of a product is given by \(\frac { dC }{ dx } \) = 100 −10x + 0.1x² where x is the output. Obtain the total and the average cost function of the firm under the assumption, that its fixed cost is Rs. 500.