Question

Approximate the integral using the trapezoidal rule, Simpson's
Simpson's 3/8 rule. Compare their results.
2 xy
-dx
7
1
0​

Answer 1

Answer:

In this Paper, we have derived the numerical integration formula for unequal data spacing. For doing so we use Newton’s Divided difference formula to evaluate general quadrature formula and then generate Trapezoidal and Simpson’s rules for the unequal data spacing with error terms. Finally we use numerical examples to compare the numerical results with analytical results and the well-known Monte- Carlo integration results and find excellent agreement.