4.4. Simpson’s 3/8 Rule

Try these first

1. 1.

   What is the formula for Simpson's 3/8 Rule?

   Hint

   Make sure to remember the sums and how the intervals are grouped.

2. 2.

   Why must n be a multiple of 3 in Simpson's 3/8 Rule?

   Hint

   Think about the pattern of the sequence of coordinates used in the calculation.

3. 3.

   What is the defining aspect of Simpson's 3/8 Rule?

   • Uses linear equations
   • Uses cubic polynomials
   • Uses triangular elements

   Hint

   Think about the types of formulas we've discussed.

4. 4.

   True or False: Simpson's 3/8 Rule can be applied when n is any integer.

   • True
   • False

   Hint

   Review the conditions needed for this method.

5. 5.

   Estimate the integral of f(x) = cos(x) from 0 to π/2 using Simpson's 3/8 Rule with n=3. Calculate the error involved.

   Hint

   Make sure to first compute the necessary function values for the approximation.

6. 6.

   Discuss the advantages of using Simpson's 3/8 Rule over the Trapezoidal Rule for approximating integrals and provide example scenarios.

   Hint

   Consider how curves behave differently from straight lines.