A function gives the rate of change of a quantity (in units per hour) with respect to…

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

A function

f

gives the rate of change of a quantity

Q

(in units per hour) with respect to time

t

(in hours). Which of the following expressions represents the net change in

Q

from

t=2

t=7

? (a)

\displaystyle \int_{2}^{7} |f(t)|\,dt

(b)

\displaystyle \int_{2}^{7} f(t)\,dt

(c)

\displaystyle 5\bigl(f(7)-f(2)\bigr)

(d)

\displaystyle \frac{1}{5}\int_{2}^{7} f(t)\,dt