Chapter 5: Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition with a graph or algebraic example, if possible. (page 494)

Q. 6

The geometric interpretations of the n2-parabola Simpson’s Rule approximation for the definite integral of a function f on an interval a,b.

Short Answer

Expert verified

SIMP(n)=f(x0)+4f(x1)+2f(x2)+4f(x3)+.....+2f(xn-2)+4f(xn-1)+f(xn)x3

Step by step solution

01

Given

fis integrable on a,band n is a positive even integer.

02

Write a mathematical definition.

Function fis integrable on a,band nis a positive even integer. Letx=b-anand xk=a+kx. Then we can approximate role="math" localid="1663211521399" abf(x)dxwith n2parabola-topped rectangles by using the following sum, which is known as Simpson’s Rule:

SIMP(n)=f(x0)+4f(x1)+2f(x2)+4f(x3)+.....+2f(xn-2)+4f(xn-1)+f(xn)x3

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