4.3. Simpson’s 1/3 Rule

Try these first

1. 1.

   What must n be in Simpson's 1/3 Rule?

   Hint

   Think about the number of intervals needed.

2. 2.

   What does h represent in the formula?

   Hint

   How do you find the width of each segment?

3. 3.

   What is the key advantage of using Simpson's 1/3 Rule compared to the Trapezoidal Rule?

   • It's simpler to compute.
   • It provides higher accuracy.
   • It's always faster.

   Hint

   Think about how shapes differ in fitting a curve.

4. 4.

   True or False: Simpson’s 1/3 Rule requires an odd number of intervals.

   • True
   • False

   Hint

   Consider what makes it effective.

5. 5.

   Estimate the integral of f(x) = e^x from 0 to 1 using Simpson’s 1/3 Rule with 4 intervals. Provide a complete solution.

   Hint

   Make sure to correctly identify your function evaluations at each breakpoint.

6. 6.

   Evaluate the error for f(x) = cos(x) over [0, π/2] using Simpson's 1/3 Rule. What does it tell you about the accuracy?

   Hint

   Recap how the fourth derivative impacts the estimation of error.