) Derive the Simpsons 1/3 rule and use it to find the integral of f(x) from Table 1 below within the interval [ 1, 3 ].                         x                        f(x)                        1.0                        2.1                        1.5                        3.2                        2.0                        3.4                        2.5                        2.8                        3.0                        2.7   ii) Find the integral of f(x) within the interval [ 1, 3 ] using Simpsons 3/8 rule. iii) Compare your answers in i) and ii) above.

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