Using the TI-85, approximate the value of

using the **Simpson's Rule** with a partition of 150 points.

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- We enter the function on the calculator:
- Subdivide
**[-1, 1]**into**150**subintervals of equal length. - The length of each of these subintervals is
which is **(1 - (-1))/150 = 1/75**. - We determine the endpoints of these subintervals:
**a**_{i}= -1 + i (1/75) = -1 + i/75 - We enter the left-hand endpoints on the calculator and store them in
the variable
**x**: - The calculator displays the list of left-hand endpoints:
- The calculator automatically stores the values of
**f(x**in the list_{i})**y1**. - We now take the sum of the list
**y1**, multiply by Dx, and store the answer in the variable**L**: - We enter the right-hand endpoints on the calculator and store them in
the variable
**x**: - The calculator displays the list of left-hand endpoints:
- Again, the calculator automatically stores the values of
**f(x**in the list_{i})**y1**. - We now take the sum of the list
**y1**, multiply by Dx, and store the answer in the variable**R**: - We take the average of the sum of the left-hand approximation and the
right-hand approximation to get the Trapezoidal Rule and we store this in
**T**:**(L+R)/2->T****1.56989143142**. - We enter the midpoints on the calculator and store them in the variable
**x**: - The calculator displays the list of midpoints:
- Again, the calculator automatically stores the values of
**f(x**in the list_{i})**y1**. - We now take the sum of the list
**y1**, multiply by Dx, and store the answer in the variable**M**:**1.57106123569**. - To get Simpson's Rule, we take the weighted average:
**(T+2*M)/3****1.57067129882**.The correct answer is

**p/2 = 1.57079...**.