TrapSimpson

TrapSimpson - Math 168 Kouba Estimating Definite Integrals...

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Unformatted text preview: Math 168 Kouba Estimating Definite Integrals l. TRAPEZOIDAL RULE 1. Divide theinterval [a, b] into n equal parts, each of length b’a « n 2. Let x o , x 1 ,x 2 , . . . ,x n be the endpoints of the subintervals. b 3. An estimate for J f(x) dx is a Tn = b"3‘[J‘(Xo)+2f(x1)+21‘(X2)+'"+21‘(Xn.1)+f(><n)] 2n 4. Absoluteerroris |En| s (b—a)3 . { max lf"(x)|} 12n2 aSXSb ll. SIMPSON'S RULE 1. Divide the interval [a, b] into n equal parts(n MUST be even !) each of length b - a ' n 2. Let xo,x1,x2,...,xn bethe endpoints ofthe subintervals. b 3. An estimate for Jflx) dx is a 8n = b‘a[f(xo)+4f(X1)+2f(X2)+4f(X3)+-'- 3“ +2f<xn-2)+4f(Xn-i)+f<xn)1. 4. Absoluteerroris IEn|S(b-a)5- max|f(4)(x)| 180n4 aSXSb Kana—m SW KW @223 . Sq 5' ) KWMm:«/7€}M m “4 x+l a? 3‘5 X+3 dL/X ~fl —q ~L: 4'é<)’3><_<.‘_i31fj “:9 ‘5 4! {L H -—q 8:— ‘33 [W w(‘9)+oz+<9+wg)+ +642] 1 7‘; [02+q<§)+1G37/)+%%+3] x 02.38425” 5 W1 S—q it; 01“: kaqzomgég .J —5 WW SE45“: g; M..ng : 0.00001 QW; QMW In MMMMM Sn I “1' x+1 759k» Wm-OQHQ 0,} 5-5 X+3 W aj’M 0.00001. ’f WW IEWI i SW QWMWW) M Cb~0k)5' M a (80 m” asxsb X“ ‘ ‘1 u -3 ‘ ~44 (q) ~48 44%): 35:33 ~3:C><):a‘<é<+3’);¥(><): *q(X+3)j4:‘éx):12(>(+3)J \(L (x): 0W3); w M [#CQ)CX)’ : 4(8 Z q? W “596'” K-lj+3i (“kt—5))? Z \1 4 HE“ E ‘30 W 48 qfn‘, _. 0.02001 ———‘7 MM ‘1 \ L <1 _ “4 3 456300001) % w?- [W) 3(1)? Vl—lq ...
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This note was uploaded on 02/17/2012 for the course MATH 16b taught by Professor Chuchel during the Winter '08 term at UC Davis.

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TrapSimpson - Math 168 Kouba Estimating Definite Integrals...

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