Question

W
UC required Cubic polynomial.
24. (a) Use Simpson's 1/3 rule, taking five ordinates, to find approximately the
value of f/x--dx upto two places of decimal.
(b) Solve the following system of linear equations by Gaussian elimination
method: 2x+y+z= -2; x+2y+z=1;x-2y-32=1 (
WesCTE 2015, 201
nswer:​

Answer 1

Simpson’s 1/3 rule of integration is exact for integrating polynomials of third order or less.

Although Simpson’s 1/3 rule is derived by approximating the integrand by a second order

polynomial, the area under the curve is exact for a third order polynomial. Without proof it can

be shown that the truncation error in Simpson’s 1/3 rule is baf ab Et << − −= ),( ζζ 2880

)( )4(

5

.

Since the fourth derivative of a third order polynomial is zero, the truncation error would be zero.

Hence Simpson’s 1/3 rule is exact for integrating polynomials of third order or less.