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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:
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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.
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