Let be a differentiable function that is increasing and concave down on

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

Problem

Let

g

be a differentiable function that is increasing and concave down on

[1,5]

. The integral

I=\displaystyle \int_{1}^{5} g(x)\,dx

is approximated with four equal subintervals by the left sum

L

and by the trapezoidal sum

T

. Which of the following relationships among

L,\,T,

and

I

must be true? (a)

T < L < I

(b)

L < I < T

(c)

L < T < I

(d)

T < I < L