Q13Advanced Engineering Mathematics

Question

Write the formulae of Trapezoidal rule and simpson 1/3 rule.

Answer 1

Trapezoidal Rule: This rule approximates the region under the graph as a trapezoid and calculates its area. The formula is $\int_{a}^{b} f (x) d x \approx \frac{h}{2} [(y_{0} + y_{n}) + 2 (y_{1} + y_{2} + \dots + y_{n - 1})]$ , where $h$ is the step size.

Simpson's 1/3 Rule: This rule uses quadratic parabolas to interpolate the function. The formula is $\int_{a}^{b} f (x) d x \approx \frac{h}{3} [(y_{0} + y_{n}) + 4 (y_{1} + y_{3} + \dots) + 2 (y_{2} + y_{4} + \dots)]$ . It requires an even number of intervals.

Q13Advanced Engineering Mathematics

Question

Answer