problema regla trapezoidal dada una integral

Método de Newton-Raphson

X	f(x)		Ecuación	=	x^2-x-2		X1	f(X1)	f'(X1)	X0	e%	Respuesta
-10	108		Ecuación derivada	=	2x-1		0	-2	-1	-2	100
-9	88		X1	=	0		-2	4	-5	-1.2	66.6666667
-8	70		e%	=	0.01		-1.2	0.64	-3.4	-1.01176471	18.6046512
-7	54						-1.01176471	0.035432526	-3.02352941	-1.00004578	1.17183924
-6	40						-1.00004578	0.000137333	-3.00009155	-1	0.00457764	-1
-5	28						-1	2.09548E-09	-3	-1	6.9849E-08	-1
-4	18						-1	0	-3	-1	0	-1
-3	10						-1	0	-3	-1	0	-1
-2	4						-1	0	-3	-1	0	-1
-1	0						-1	0	-3	-1	0	-1
0	-2						-1	0	-3	-1	0	-1
1	-2						-1	0	-3	-1	0	-1
2	0						-1	0	-3	-1	0	-1
3	4						-1	0	-3	-1	0	-1
4	10						-1	0	-3	-1	0	-1
5	18
6	28
7	40
8	54
9	70
10	88

matlab

function x = Newt_n(f_name, xO)

% Iteración de Newton sin gráficos

x = xO; xb = x-999;

n=0; del_x = 0.01;

while abs(x-xb)>0.000001

  n=n+1; xb=x ;

  if n>300 break; end

  y=feval(f_name, x) ;

  y_driv=(feval(f_name, x+del_x) - y)/del_x;

  x = xb - y/y_driv ;

  fprintf(' n=%3.0f, x=%12.5e, y=%12.5e, ', n,x,y)

  fprintf(' yd = %12.5e \n', y_driv)

end

fprintf('\n Respuesta final = %12.6e\n', x) ;

f(x) = (x – 3) (x – 1) (x – 1)

n	xn	f(xn)	f'(xn)	xn+1
0	0.50000000	-0.62500000	2.75000000	0.72727273
1	0.72727273	-0.16904583	1.31404959	0.85591767
2	0.85591767	-0.04451055	0.63860849	0.92561694
3	0.92561694	-0.01147723	0.31413077	0.96215341
4	0.96215341	-0.00291894	0.15568346	0.98090260
5	0.98090260	-0.00073639	0.07748373	0.99040636
6	0.99040636	-0.00018496	0.03865069	0.99519176
7	0.99519176	-0.00004635	0.01930234	0.99759300
8	0.99759300	-0.00001160	0.00964539	0.99879578
9	0.99879578	-0.00000290	0.00482125	0.99939771
10	0.99939771	-0.00000073	0.00241026	0.99969881

metodo de falsa posición

	X	f(x)			Ecuación	=	exp(x)-3x
	-10	30.0000454			X1	=	0
	-9	27.00012341			X2	=	1
	-8	24.00033546			e%	=	0.01
	-7	21.00091188
	-6	18.00247875					X1	X2	Xm	f(X1)	f(X2)	f(Xm)	e%	Respuesta
	-5	15.00673795					0.000000000	1.000000000	0.500000000	1	-0.28171817	0.14872127	100.0
	-4	12.01831564					0.500000000	1.000000000	0.750000000	0.14872127	-0.28171817	-0.13299998	33.3
	-3	9.049787068					0.500000000	0.750000000	0.625000000	0.14872127	-0.13299998	-0.00675404	20.0
	-2	6.135335283					0.500000000	0.625000000	0.562500000	0.14872127	-0.00675404	0.06755466	11.1
	-1	3.367879441					0.562500000	0.625000000	0.593750000	0.06755466	-0.00675404	0.02951607	5.3
	0	1					0.593750000	0.625000000	0.609375000	0.02951607	-0.00675404	0.01115649	2.6
	1	-0.281718172					0.609375000	0.625000000	0.617187500	0.01115649	-0.00675404	0.00214465	1.3
	2	1.389056099					0.617187500	0.625000000	0.621093750	0.00214465	-0.00675404	-0.00231889	0.6
	3	11.08553692					0.617187500	0.621093750	0.619140625	0.00214465	-0.00231889	-9.0663E-05	0.3
	4	42.59815003					0.617187500	0.619140625	0.618164063	0.00214465	-9.0663E-05	0.00102611	0.2
	5	133.4131591					0.618164063	0.619140625	0.618652344	0.00102611	-9.0663E-05	0.0004675	0.1
	6	385.4287935					0.618652344	0.619140625	0.618896484	0.0004675	-9.0663E-05	0.00018836	0.0
	7	1075.633158					0.618896484	0.619140625	0.619018555	0.00018836	-9.0663E-05	4.8837E-05	0.0
	8	2956.957987					0.619018555	0.619140625	0.619079590	4.8837E-05	-9.0663E-05	-2.0917E-05	0.0	0.61907959
	9	8076.083928					0.619018555	0.619079590	0.619049072	4.8837E-05	-2.0917E-05	1.3959E-05	0.0	0.619049072
	10	21996.46579					0.619049072	0.619079590	0.619064331	1.3959E-05	-2.0917E-05	-3.4791E-06	0.0	0.619064331

X	f(x)			Ecuación	=	3x^2-3x+1
-10	231			X1	=	0
-9	190			X2	=	1
-8	153			e%	=	0.01
-7	120
-6	91					X1	X2	Xm	f(X1)	f(X2)	f(Xm)	e%	Respuesta
-5	66					0.000000000	1.000000000	0.500000000	0	1	0	100.0
-4	45					1.000000000	0.010000000	0.505000000	-0.00495	1.01489901	0.01534297	100.0
-3	28					0.010000000	0.000000000	0.005000000	0.98505	-0.01450299	1.04392966	100.0
-2	15					0.000000000	X1	0.000000000	1	0	1	100.0
-1	6					X1	0.000000000	0.000000000	1	0	1	100.0
0	1					0.000000000	1.000000000	0.500000000	0	1	0	100.0
1	0					1.000000000	0.010000000	0.505000000	-0.00495	1.01489901	0.01534297	100.0
2	3					0.010000000	0.000000000	0.005000000	0.98505	-0.01450299	1.04392966	100.0
3	10					0.000000000	X1	0.000000000	1	0	1	100.0
4	21					X1	0.000000000	0.000000000	1	0	1	100.0
5	36					0.000000000	1.000000000	0.500000000	0	1	0	100.0
6	55					1.000000000	0.010000000	0.505000000	-0.00495	1.01489901	0.01534297	100.0
7	78					0.010000000	0.000000000	0.005000000	0.98505	-0.01450299	1.04392966	100.0
8	105					0.000000000	X1	0.000000000	1	0	1	100.0
9	136					X1	0.000000000	0.000000000	1	0	1	100.0
10	171					0.000000000	1.000000000	0.500000000	0	1	0	100.0

X f(x) Ecuación = x^4+20 -10 10020 X1 = 0 -9 6581 X2 = 1 -8 4116 e% = 2 -7 2421 -6 1316 X1 X2 Xm f(X1) f(X2) f(Xm) e% Respuesta -5 645 0.000000000 1.000000000 0.500000000 20.0625 162029.395 6.8925E+20 100.0 -4 276 1.000000000 2.000000000 1.500000000 25.0625 394565.923 2.4237E+22 100.0 -3 101 2.000000000 0.000000000 1.000000000 21 194501 1.4312E+21 100.0 -2 36 0.000000000 X1 0.000000000 20 160020 6.5569E+20 100.0 -1 21 X1 0.000000000 0.000000000 20 160020 6.5569E+20 100.0 0 20 0.000000000 1.000000000 0.500000000 20.0625 162029.395 6.8925E+20 100.0 1 21 1.000000000 2.000000000 1.500000000 25.0625 394565.923 2.4237E+22 100.0 2 36 2.000000000 0.000000000 1.000000000 21 194501 1.4312E+21 100.0 3 101 0.000000000 X1 0.000000000 20 160020 6.5569E+20 100.0 4 276 X1 0.000000000 0.000000000 20 160020 6.5569E+20 100.0 5 645 0.000000000 1.000000000 0.500000000 20.0625 162029.395 6.8925E+20 100.0 6 1316 1.000000000 0.500000000 0.750000000 -0.28171817 0.14872127 -0.13299998 33.3 7 2421 0.750000000 0.500000000 0.625000000 -0.13299998 0.14872127 -0.00675404 20.0 8 4116 0.625000000 0.500000000 0.562500000 -0.00675404 0.14872127 0.06755466 11.1 9 6581 0.625000000 0.562500000 0.593750000 -0.00675404 0.06755466 0.02951607 5.3 10 10020 0.625000000 0.593750000 0.609375000 -0.00675404 0.02951607 0.01115649 2.6