Question

Use the table of values to estimate S ^6 0 f(x) dx, use three equal subintervals and the

(only solve part D)

1. Left end points
2. Right end points
3. Midpoints

When f is an increasing function, how does each estimate compare with the actual value? Explain your reasoning

x	0	1	2	3	4	5	6
F(x)	-6	0	8	18	30	50	80

 

D. Also find L6, R6, T3, and T6. Remember that Tn is the average of Ln and Rn. Finally, use your calculator to do quadratic regression to find a decent model for your data [let’s call it q(x)] and have your calculator approximate S ^6 0 q (x) dx

Answer 1

(D) We recall that is the approximation using subintervals and taking the value of the function at the left endpoint. Also, is the approximation using subintervals and taking the value of the function at the right endpoint. Finally, .

Threfore,

.

Anagolously,

.

Now we use a calculator to obtain a regression. In particular, we use the command of MATLAB to approximate the data by a degree 2 polynomial. The result is

.

We have .