ACOW INDEFINITE INTEGRALS MODULE Updated 5/28/2016 Page 1 of 1 Activity A4- Applications of Integration Let S ( x ) represent the total daily sales for a company. If we want to find the company’s instantaneous rate of change of sales, then we would compute S '( x) s( x) . Now that we know about antiderivatives, we can be given a company’s rate of change of sales function s ( x ) and find its total sales function S ( x ) . 1. a) The rate of change in sales of bicycles at Ted’s bicycle shop for the year 2001 is given by s ( x) 0.5 x 4 , where x represents the month number in 2001 (i.e. x = 1 is January, x = 2 is February, …, x = 12 is December). Find the shops total sales function, TS ( x) . b) If Ted’s bicycle shop sold 25 bicycles in the month of March, how many did the shop sell in April? 2. A company’s marginal profit function, in thousands of dollars, is given by MP( x) 0.09 x 2 2.6 x 15.9 , where x is the number of hundreds of items sold. If the company’s profit is $38,000 when 1000 items are sold, find the company’s profit function. 3 a) A L&L lighting company has a marginal revenue function, in dollars, given by MR( x) 0.4 x 60 , where x is the number of lamps sold. Find the company’s revenue function. (Hint: When a company does not sell any items it does not generate any revenue.) b) If the L&L lighting company’s profit function, in dollars, is given by P( x) 0.25 x 2 30 x 500 , where x is the number of lamps sold, use the information found in 2a) to determine the total cost for the company to produce 40 lamps.