Question: 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

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.


5 4 3. 2 y 1 f 2 x 5 4 3



(a) Using the Trapezoidal Rule with n = 4, which integral would be overestimated,


2 1 y 1 g 2 X


Which integral would be underestimated? Explain your reasoning.


(b) Which rule would you use for more accurate approximations of


image


the Trapezoidal Rule or Simpson’s Rule? Explain your reasoning.

5 4 3. 2 y 1 f 2 x 5 4 3 2 1 y 1 g 2 X

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