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Problem: Trapezoidal Simpson rule, {{0.0,1.0000},{0.1,0.9975},{0.2,0.9900},{0.3,0.9776},{0.4,0.8604}} [ Calculator, Method and examples ]

Solution:
Your problem `->` Trapezoidal Simpson rule, {{0.0,1.0000},{0.1,0.9975},{0.2,0.9900},{0.3,0.9776},{0.4,0.8604}}


The value of table for `X` and `Y`

X00.10.20.30.4
Y10.99750.990.97760.8604

Using Trapezoidal Rule
`int Y dx = h/2 (y_0 + 2 (y_1 + y_2 + y_3) + y_4 )`

`int Y dx = 0.1/2 (1 + 2 xx (0.9975 + 0.99 + 0.9776) + 0.8604 )`

`int Y dx = 0.1/2 (1 + 2 xx (2.9651) + 0.8604 )`

`int Y dx = 0.38953`

Solution By Trapezoidal Rule is `0.38953`



Using Simpsons `1/3` Rule

`int Y dx = h/3 (y_0 + 4(y_1 + y_3) + 2(y_2) + y_4 )`






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