Let represent the rate

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

R(t)

represent the rate, in pounds per minute, at which sand is deposited on a beach, where

t

is measured in minutes. Which of the following best describes the quantity

\displaystyle \int_{0}^{20} R(t)\,dt

? (a)

20

times the instantaneous rate at which sand is deposited at

t=20

, expressed in pounds (b) The total amount of sand, in pounds, that would be deposited if the rate remained constant at its initial value

R(0)

for the

20

-minute interval (c) The total amount of sand, in pounds, deposited during the first

20

minutes (d) The average amount of sand, in pounds, deposited per minute during the first

20

minutes