Math 241 Approximation Sec5_ 9

Math 241 Approximation Sec5_ 9 - Trapezoid’s Rule Drawing...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 241 Approximation Methods Section 5.9 Outline of Lecture We use approximation methods for one of two reasons, -we cannot find (it is impossible to find for some functions) an antiderivative for the integrand function - we have data instead of an algebraic definition for our function Midpoint Rule Trapezoidal Rule Simpson’s Rule First, remember the definition of the definite integral & the picture f ( x ) dx = lim n "# f ( x i ) $ x i = 1 n % a b Draw picture of left and right and rectangles for an unknown curve; discuss why midpoint is better than using left or right endpoints. Midpoint Rule written in text Picking midpoint to draw rectangles
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Trapezoid’s Rule Drawing trapezoid’s to approximate the area Simpson’s Rule Based on drawing a parabola from the 3 points in each subinterval Simpson’s rule gives the best approximation Example 1 Use all three methods with n=8 to approximate x sin xdx 4 " Fill in the following table with your calculator (make sure you’re in radian mode) X f(x)= x sin x 0 .5 1 1.5 2 2.5 3 3.5 4 a) Find the Trapezoid’s Rule Approximation b) Find the Midpoint Rule Approximation c) Find the Simpson’s Rule Approximation. Example 2 - #26 p.422 of our text – radar gun data problem...
View Full Document

This note was uploaded on 01/25/2012 for the course MA 241 taught by Professor Mccollum during the Spring '08 term at N.C. State.

Page1 / 2

Math 241 Approximation Sec5_ 9 - Trapezoid’s Rule Drawing...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online