Ganitagya Gyanam

1. The process of evaluating a definite integral from a set of tabulated values of the integrand is known as A) Numerical Integration B) Quadrature C) Numerical Differentiation D) None ... Answer is A) Numerical Integration Show Answer 2. The process when applied to a function of a single variable, is known as A) Numerical Integration B) Quadrature C) Numerical Differentiation D) None ... Answer is A) Numerical Integration Show Answer 3. Simpson's one-third is derived by newton cotes if n is A) 2 B) 3 C) 4 D) 5 ... Answer is A) 2. Show Answer 4. Simpson's three-eighth is derived from newton cote's if n is A) 2 B) 3 C) 4 D) None ... Answer is B) 3" Show Answer 5. Simpsons one-third rule is used only when A) n is even B) The ordinates is even C) n is multiple of 3 D) n is odd ... Answer is A) n is ...

 Simpson's three-eighths rule is a very important rule in numerical integration. In this case, we subdivide [a, b] into a number of subintervals of equal length such that the number of subintervals is divisible by 3. That is, the number of intervals must be 6 or 9 or 12, etc. so that we get 7 or 10 or 13 nodal points, etc.  Simpson's 3/8th rule has some disadvantages.  i) The number of subintervals must be divisible by 3. ii) It is of the same order as Simpson's 1/3rd rule which only requires that the number of nodal points must be odd iii) The error constant c in the case of Simpson's 3/8th rule is c=3/80 , which is much larger than the error constant c=1/90 , in the case of Simpson's 1/3rd rule. Therefore, the error in the case of Simpson's 3/8th rule is larger than the error in the case of Simpson's 1/3rd rule. due to these disadvantages, Simpson's 3/8th rule is not used in practice.

Simpson's one-third formula provides a more accurate result as compared to the trapezoidal method.  Simpson's rule integrates exactly polynomials of degree ≤ 3. Therefore, the method is of order 3.