A continuous and non-negative function satisfies

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

Problem

A continuous and non-negative function

g

satisfies

\displaystyle \int_{0}^{4} g(x)\,dx =15

. Which of the following statements must be true? (a) There exists a number

c

(0,4)

such that

g(c)=15

. (There is a point on the graph whose

y

-coordinate equals the value of the integral.) (b) The total change in

g

over

[0,4]

15

units. (c) The average value of

g

on the interval

[0,4]

15

. (d) The region bounded by the graph of

g

, the

x

-axis, and the lines

x=0

and

x=4

has area

15

square units.