Question

How could the definite integral be used to determine profit over a given period?

Answer 1

Answer:

P(b) - P(a) = ∫P'(t)dt  (from t = a to t = b)

Step-by-step explanation:

Suppose that

P(t) denotes the profit of any business after time t years  then

P(t) = total profit after t years

If you want to collect the profit for the some time interval like (a , b)          where a < b then you just need to subtract the corresponding values of function of P(t) at b and a That is

P(b) - P(a)

And we know by calculus for any function P(t)

P(b) - P(a) = ∫P'(t)dt  (from t = a to t = b)

where P'(t) denote the derivative of P(t)

So

In this way integral of P(t) on the interval (a , b) gives us the profit of years between a and b.