Math 241 Approximation Sec5_ 9

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

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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

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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...
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## 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.

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

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