A function is positive

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

Problem

A function

f

is positive, increasing, and concave down on the interval

[1,5]

. The interval is divided into four equal subintervals of length

1

. Four different numerical estimates for

\displaystyle\int_{1}^{5} f(x)\,dx

are obtained: (a) III only (b) IV only (c) II only (d) II and III