Values of a continuous function are given in the table

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

Problem

Values of a continuous function

s

are given in the table.

x	0	2	4
s(x)	3	2	0

Assume

s

is decreasing and concave down on

[0,4]

. Let

t(x) = -0.5x + 4

on the same interval. Using the trapezoidal rule with subintervals

[0,2]

and

[2,4]

to approximate

\int_{0}^{4} s(x)\,dx

, which statement accurately compares the average values of

s

and

t

[0,4]

? (a) The average values of

s

and

t

are equal. (b) The average value of

s

is greater than the average value of

t

. (c) The average value of

s

is less than the average value of

t

. (d) The relationship between the averages cannot be determined from the given data.