Q9Advanced Engineering Mathematics I

Question

Write the formulae of Simpson 1/3 rule and Simpson 3/8 rule.

Answer 1

Let the interval $[a, b]$ be divided into $n$ equal sub-intervals of width $h = \frac{b - a}{n}$ .

Simpson's 1/3 Rule (requires $n$ to be even): $\int_{a}^{b} f (x) d x \approx \frac{h}{3} [(y_{0} + y_{n}) + 4 (y_{1} + y_{3} + \dots) + 2 (y_{2} + y_{4} + \dots)]$

Simpson's 3/8 Rule (requires $n$ to be a multiple of 3): $\int_{a}^{b} f (x) d x \approx \frac{3 h}{8} [(y_{0} + y_{n}) + 3 (y_{1} + y_{2} + y_{4} + y_{5} + \dots) + 2 (y_{3} + y_{6} + \dots)]$

Q9Advanced Engineering Mathematics I

Question

Answer