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Unformatted text preview: parabola uniquely? How many subintervals do these three points create? As a result, in order to apply Simpson’s rule the number of subintervals ( n ) MUST be . x x 1 x 2 x y 4 Deﬁnition Simpson’s Rule To approximate Z b a f ( x ) dx use: S Simp = where y i = f ( x i ), Δ x = ba n and n is an even number of subintervals Example 3 Approximate Z 2 1 sin ( e x ) dx , n = 6 x f ( x ) S Simp = Example 4 Approximate Z 4 1 √ x dx , n = 4 x f ( x ) S Simp = 5 Example 5 To do Using the following table of values approximate Z3 f ( x ) dx x32.521.510.5 f ( x ) 2 1 1 1 2 3 • Using trapezoidal rule, T = • Using Simpson’s rule, S Simp = Example 6 To do Set up the Simpson’s rule approximation for the integral Z 9 3 x x dx , n = 4. Do not evaluate...
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This note was uploaded on 10/02/2011 for the course MATH 1206 taught by Professor Llhanks during the Fall '08 term at Virginia Tech.
 Fall '08
 LLHanks
 Derivative

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