For a quantity whose rate of change is given by a continuous function (units per…

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

Problem

For a quantity whose rate of change is given by a continuous function

r(t)

(units per hour) and whose initial amount is zero, the accumulated amount after

t

hours is

A(t)=\displaystyle\int_{0}^{t} r(s)\,ds

. To find the time

T

at which the accumulated amount first equals a fixed value

K

units, which of the following equations should be solved for

T

? (a)

r(T)\,T = K

(b)

\displaystyle\int_{T}^{0} r(s)\,ds = K

(c)

\displaystyle\int_{0}^{T} r(s)\,ds = K

(d)

\displaystyle\int_{0}^{T} |\,r(s)\,|\,ds = K