Question

Difference between simpson's 1/3 rule and 3/8 rule

Answer 1

Simpson's 1/3 rule is applied when N is an even number and the Simpson's 3/8 rule is applied when N is a multiple of 3.

Answer 2

Answer:

Difference between the simpson's 1/3 rule and 3/8 rule

1) simpson's ¹/₃ rule is applicable when if the total number of interval is even whereas simpson's ³/₈ rule is applicable when if the total number of interval is multiple of 3.

2) simpson's ¹/₃ formula :  ₐ∫ᵇ f ( x ) dx =    h/₃ [ ( y₀ + yₙ ) +  4 ( y₁ + y₃ + ....) + 2 ( y₂ + y₄ + ....) ]  

here, y₀ means first terms and yₙ means last terms.

( y₁ + y₃ + .... ) means summation of odd terms.

( y₂ + y₄ + ....) means summation of even terms.

simpson's 3/8 rule :    ₐ∫ᵇ f ( x ) dx =   3h/₈  [ ( y₀ + yₙ ) + 3 ( y₁ + y₂ + y₄ + ..... ) + 2 ( y₃ + y₆ +.........) ]