ACOW INDEFINITE INTEGRALS MODULE
Updated 5/28/2016
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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.