Math 241 Approximation Sec5_ 9

Math 241 Approximation Sec5_ 9 - Trapezoids 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: Trapezoids Rule Drawing trapezoids to approximate the area Simpsons Rule Based on drawing a parabola from the 3 points in each subinterval Simpsons 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 youre in radian mode) X f(x)= x sin x 0 .5 1 1.5 2 2.5 3 3.5 4 a) Find the Trapezoids Rule Approximation b) Find the Midpoint Rule Approximation c) Find the Simpsons Rule Approximation. Example 2 - #26 p.422 of our text radar gun data problem...
View Full Document

Page1 / 2

Math 241 Approximation Sec5_ 9 - Trapezoids 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