Question

while applying Simpson’s three-eight rule , to number of sub-intervals should be taken as -

a.multiple of 2

b.multiple of 3

c.multiple of 4

d.multiple of 5

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Answer 1

Explanation:

Another method of numerical integration method is called “Simpson’s 3/8 rule”. It is completely based on the cubic interpolation rather than the quadratic interpolation. Simpson’s 3/8 or three-eight rule is given by:

∫ab f(x) dx = 3h/8[(y0+yn)+3(y1+y2+y4+y5+….+yn-1)+2(y3+y6+y9+…..+yn-3)]

This rule is more accurate than the standard method, as it uses one more functional value. For 3/8 rule, the composite Simpson’s 3/8 rule also exists which is similar to the generalized form. The 3/8 rule is known as Simpson’s second rule of integration.