14. (6 pts) Suppose f is continuous on [1,9]. Use the table of values of f to estimate
$$\int_{1}^{9} f(x)dx$$ using
left, right, and midpoint Riemann sum with n = 4. Failure to show all algebraic steps to find the
solution will result in a reduction of all possible points.
x
1 2 3 4 5 6 7 8 9
f(x) -4 -3 -2 0 2 3 6 0 -1
I.
$$\int_{1}^{9} f(x)dx \approx R_4 = \lim_{n \to \infty} \sum_{i=1}^{4} f(x_i) \Delta x = $$
II.
$$\int_{1}^{9} f(x)dx \approx L_4 = \lim_{n \to \infty} \sum_{i=1}^{4} f(x_{i-1}) \Delta x = $$
III.
$$\int_{1}^{9} f(x)dx \approx M_4 = \sum_{i=1}^{4} f(x_i) \Delta x = $$