Simpsons 1/3 Rule

Simpson’s 1/3 Rule:

Setting n = 2 in Newton’s Cotes Quadrature Formula, we obtain

For susequent intervals, similarly,

On adding all the above results,

which is known as Simpson’s 1/3 Rule. This rule requires an even number of subintervals of width h.

Example-1 The velocity v (metre/sec) of a particle at distance x (metre) is given in tabulated form:

Using simpson’s 1/3 rule, find the time taken by the particle to travel 60 metre.

Solution: We know that

Hence the time taken to travel 60 metre is

Since given data in table is for v, so now we preapre the table for 1/v, because, here f (x) = 1/v. Therefore

Now Simpson’s 1/3 rule gives,

Hence the time taken to travel 60 metre is 1.064 sec.