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

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

The value of table for X and Y

 X Y 0 0.1 0.2 0.3 0.4 1 0.9975 0.99 0.9776 0.8604

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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