The function b(t) gives the number of books sold by a store by time t (in days) of a given year. What does int_(45)^(50)b^(')(t)dt represent? Choose 1 answer: (A) The number of books sold between day 45 and day 50 (B) The total number of books sold by day 50 (C) The change in the rate of selling books between t=45 and t=50 (D) The number of days it takes to sell 50 books

Question

The function  b(t) gives the number of books sold by a store by time  t (in days) of a given year. What does  int_(45)^(50)b^(')(t)dt represent? Choose 1 answer: (A) The number of books sold between day 45 and day 50 (B) The total number of books sold by day 50 (C) The change in the rate of selling books between  t=45 and  t=50 (D) The number of days it takes to sell 50 books

Bytelearn · Accepted Answer

Fundamental Theorem of Calculus: The integral of a derivative function over an interval gives us the net change in the original function over that interval. This is a direct application of the Fundamental Theorem of Calculus.Book Sales Representation: In this context, b(t) represents the number of books sold by a store at time t, and b'(t) is the derivative of b(t), which represents the rate of change of books sold at time t. Therefore, the integral from 45 to 50 of b'(t) dt represents the net change in the number of books sold from day 45 to day 50.Matching with Options: We can now match this understanding with the given options. The net change in the number of books sold from day 45 to day 50 corresponds to the number of books sold between day 45 and day 50, which is option (A).

Full solution

More problems from Find derivatives of sine and cosine functions

Related topics