TrapSimpson

# TrapSimpson - Math 168 Kouba Estimating Definite Integrals...

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

## 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.

### Page1 / 2

TrapSimpson - Math 168 Kouba Estimating Definite Integrals...

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

View Full Document
Ask a homework question - tutors are online