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# TrapSimp - Math 218 Kouba Estimating the Value of a...

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Unformatted text preview: Math 218 Kouba Estimating the Value of a Deﬁnite Integral b Suppose that the integral / f (11:) da: is too difﬁcult (or impossible) to compute, or that you a are simply required to estimate its exact value. The following two methods offer possible ways to compute an estimate and measure its accuracy. 1.) TRAPEZOIDAL RULE b—a a.) Divide the interval [a, b] into 11 equal parts, each of length h = n b.) Let a = m0, 3:1, 1:2, 3:3, ..., \$71-1, at” = b be the partition of the interval. b c.) The Trapezoidal Estimate for / f (ac) due is Tn Wino) +2f(\$1) +2f(\$2) + +2f(\$n—1) +f(\$n)l h 2 2 d.) The Absolute Error is |En| S (b — a)%{ mairb |f”(x)|} . 2.) SIMPSON’S RULE (NOTE: For this method n MUST be an even integer !) b—a a.) Divide the interval [(1, b] into n equal parts, each of length h = n b.) Let a = x0, x1, x2, x3, ..., mn_1, run 2 b be the partition of the interval. b c.) The Simpson Estimate for / f (m) d1: is Sn = % ”(130)+4f(\$1)+2f(\$2)+4f(\$3)+---+4f(\$n—3)+2f(33n—2)+4f(\$n—1)+f(\$n)l h4 d.) The Absolute Error is |En| S (b — a)—1-é-6{ arggécb |f(4)(m)|} . V5 ><+3 —ﬁ vq -£ +C2X—zf-éw '5 4’ ‘1 ‘4 ‘4 —-—+————r——~———r—————4\—+~—— 8‘5 '32)” [4652+ «#(‘gkwwwvgjwt w] r; [4+q<§)+i<‘9+q(‘33)+3] z 02.38605 x+l —4 W1 \$5 ><+3 M ~“— Hﬂqu’ozagég . J (I 5 WW “242:21: £1”; 400- 54’ 2 0.00001 5“ 5W wa (/1 W M 769k; WW «4 L44 ‘ J ”T 3-5 ><+3 M MW’ W aim 0.00001. ? WW [Em] i Cb~a)5' M {‘PGJQX), .__>, [50 m“! QiX'Sb _ 35:1— ‘ ~ ~2 u “3 \l( «q (q) ‘98 ~98)» x+sj~¥CX)—JLQ<+3)J\$CX): ~q(X+3jj—Pé<): 12093)] 4 (X): (X44); w M qubdl : Q8" 5, Z <43 J ﬂan/y “55X5’q {640+3l < -q‘C—_5’))5i I ‘2‘ m ‘ w «a? W i % MM 4 \1, UL ‘* _ V‘ 3 450330001) ‘2' “3 [4510 00°C!) ~ (1-7 WW H ...
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TrapSimp - Math 218 Kouba Estimating the Value of a...

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