Which of the following formulae is Simpson's 3/8th rule for numerical integration?

P (0, 3), Q (0.5, 4), and R (1, 5) are three points on a curve. Numerical integration is carried out using both the Trapezoidal rule and Simpson's 1/3rd rule within limits x=0 and x=1 for the curve. The difference between the two results will be 

Match the following numerical integration schemes with the correct polynomial order used to fit the data.

Which of the following can exactly determine the integral of a 5th-order polynomial with a single application?

Evaluate  using Simpson's 3/8th rule. 

Use the data from the following table.

Which of the following statements is true regarding the number of points for the Simpson’s 3/8 rule?

Which of the following is true for the truncation error in the single Simpson's 1/3 rule?

What is the approximate value of the following integral using a single application of Simpson’s 1/3 rule?

f(x) = ∫ (x^3 - 8x^2) dx, integrate from x = 0 to x = 9

Simpson's 1/3rd rule and direct integration would generate the same result if 

Integrate the following data using the trapezoidal rule. What is the output? 

   x_i = [-5  -4.5  -4  -3.5]
f(x_i) = [ 8    5    6    5 ]