Chapter 8.8, Problem 77E

  Trapezoid Rule and concavity Suppose f is positive and its first two derivatives are continuous on [a, b] If f ’ is positive on [a, b], then is a Trapezoid Rule estimate of ${\displaystyle {\int }_a^{b}f(x)}$ dx an underestimate or overestimate of the integral? Justify your answer using Theorem 8.1 and an illustration.