7/26/2019 Problema 3 de Metodos Numericos

1/4

a) 2

4

(1x4x3+2x5 ) dx = x| 4

2

1

2x

2| 42

x4| 42

+1

3x

6| 42

24 ) 12

(164 )(25616 )+ 13(409664)

6

4032

6240+1

3 ) =

240+1344=1104

b) y c) son lo mismo

FRMULA DE LA REGLA DEL TRAPECIO

x =ba

n ;xi=a+i x , para i = 0, 1,

., n

A T = x

2 [f( x0+2 f(x1 )+2 f(x2 )+ + 2f( xn1 + f(

xn

n=2

x =4(2)

4=6

4=3 xi=a+i x , para i = 0, 1, ., n

x0 = -2+0(3) = -2

x1 = -2+(1)(3)=1

x2 = -2 +(2)(3)=4

7/26/2019 Problema 3 de Metodos Numericos

2/4

f(x )=1x4x3+2x5

f(2 )=1(2)4 (2)3+2(2)5 = -29

f(1 )=114(1)3+2(1)5 =-2

f( 4 )= 1-4-4( 43 +2 (4 )

5

=1789

A T =3

2 [-29+ 2 (2 )+ 1789 =3

2[1756 ]= 263

n=4

x =4(2)

4=

6

4=3

2 xi=a+i x , para i = 0, 1, ., n

x0 = -2+(0)(

3

2 ) = -2

x1 = -2+(1)(

3

2 )= -12

x2 = -2+(2)(

3

2 = 1

x3 = -2+(3)(

3

2=

5

2

x4 = -2+(4)(

3

2= 4

f(x0 )=f(2)=1(2)4 (2)3+2(2)5 = -29

f(x1 )=f(1/2)= (1/2)4(1/2)3+2(1 /2)5 = 1,937!

f(x2 )=f(1)= 1 (1 )4 (1 )3+2 (1 )5=2

f(x3 )=f(5 /2)= 1(5/2)4 (5/2)3+2(5/2)5 =131,312!

f(x4 )=f(4 )= 1(4)4 (4 )3+2(4)5 =1789

AT = x2 [f( x0+2 f(x1 )+2 f(x2 )+ + 2f( xn1 + f(

xn A T=3

4 [-29+2(1,937!)+2(-2)+2(131,312!)+1789"

AT= 1!16"87!

7/26/2019 Problema 3 de Metodos Numericos

3/4

#)con $na sola aplicacion #% la r%&la #% 'impson

13FRMULA DE LA REGLA DE #IMP#O$ 1%3

A&')*& n=6 (En &, ./0 n &.. n4&.)n,5

x =ba

n xi=a+i x , para i = 0, 1, ., n

AS = x

3 [

f(x0 )+4 f(x1 )+2 f(x2 )++4 f(x3 )++2 f(x4 )++2 f(xn2 )++4 f(xn1 )+ f(xn )

n=2 x =

4(2)6

=6

6=1 xi=a+i x ,

x0 = -2+(0)( 1 = -2

x1 = -2+(1)( 1 ) = -1

x2 = -2+(2)(1)=0

x3 = -2+(3)(1) = 1

x4 = -2+(4)(1)= 2x

5 = -2+(!)(1) = 3x

6 = -2+(6)81)=4

f(x0 )=f(2)=1(2)4 (2)3+2(2)5 = -29

f(x1 )=f(1)= 1(1)4(1)3+2(1)5 =4

f(x2 )=f(0)= 1(0)4 (0)3+2(0)5 = 1

f(x3 )=f(1)= 1(1 )4 (1 )3+2 (1 )5=2

f(x4 )=f(2)= 1(2 )4 (2 )3+2 (2 )5=31

f(x5 )=f(3)= 1(3 )4 (3 )3+2 (3 )5= 376

f(x6 )=f(4)= 1(4)4 (4 )3+2(4)5 = 1789

7/26/2019 Problema 3 de Metodos Numericos

4/4

AS = x

3 [

f(x0 )+4 f(x1 )+2 f(x2 )+4 f(x3 )+2 f(x4 )++2 f(xn2)++4 f(xn1 )+ f(xn )

AS =1

3 [-29+4(4)+2(1)+4(-2)+2(31)+4(376)+1789"

AS =1

3 [3336=1112