Download Presentation
## Simpson’s Rule

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Simpson’s Rule**Let f be continuous on [a, b]. Simpson’s Rule for approximating is**Deriving Simpson’s Rule**• Remember from Algebra 2 that you can create a parabola through any three given points. • If we choose two consecutive subintervals and the three corresponding points on the function, then we can create a parabola through those points.**We could then find the area under the parabola to**approximate the area under the curve over the two subintervals.**Just like in Algebra 2, substitute each point into the**general form of a quadratic equation to create a system of three equations.**Simplify by solving the system:**Now integrate**Therefore, since [-h, h] is really [x0, x2]**and h = x, then can be changed into**Applying Simpson’s Rule below from x0 to x6**we get Generalizing Simpson’s Rule, we get**Example**Approximate using Simpson’s Rule if n = 4.