Chapter 8.6, Problem 38E

HOW DO YOU SEE IT? The function f is concave upward on the interval [0, 2] and the function g is concave downward on the interval [0,2] as shown in the figure.

(a) Using the Trapezoidal Rule with $n=4$, which integral would be overestimated, ${\displaystyle {\int }_0^{2}f(x)dx}$ or ${\displaystyle {\int }_0^{2}g(x)dx?}$

Which integral would be underestimated? Explain your reasoning.

(b) Which rule would you use for more accurate approximations of ${\displaystyle {\int }_0^{2}f(x)dx}$ and ${\displaystyle {\int }_0^{2}g(x)dx}$, the Trapezoidal Rule or Simpson's Rule? Explain your reasoning.