Albert Einstein

Carlos Eduardo Amaris 42101028 Leidy Usuga Higuita 43101046 1. Integral de (2 sin x)=xentre -1 y -2 por regla de punto medio y n=8 z
2.0

y

1.5

1.0

0.5

0.0 -2.0 -1.9 -1.8 -1.7 -1.6-1.5 -1.4 -1.3 -1.2 -1.1 -1.0

x

f (x) = (2 sin x)=x x = 1 ( 2)=8 = 0:125 x f (x) R 1:95 0:95 1:825 1:06 1:7 1:17 1:575 1:27 1:45 1:37 1:325 1:46 1:2 1:55 1:075 1:76

= 1:32375

1 (2 sinx)=xdx 2

= 0:125 (0:95+1:06+1:17+1:27+1:37+1:46+1:55+1:76)

Valor con n=500:(2 sin x)=x Approximate integral (midpoint rule) is1: 318 7 2. Integral de (2.sinx)/x entre -1 y -2 por extremos izquierdosy n=8

2.0

y

1.5

1.0

0.5

0.0 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1.0

x

1

f (x) = (2 sin x)=x x = 1 ( 2)=8 = 0:125 x 2 f (x) 0:90 R 1:875 1:01 1:75 1:121:625 1:23 1:5 1:33 1:375 1:43 1:25 1:52 1:125 1:60 1 1:68

1:2675

1 (2 sin x)=xdx 2

t 0:125(0:90+1:01+1:12+1:23+1:33+1:43+1:52+1:60) t

Valor con n=500 (2 sin x)=x Approximate integral (leftboxes) is1: 317 9 3. Integral de (2.sinx)/x entre -1 y -2 por extremos derechos y n=8 (2 sin x)=x
2.0

y

1.5

1.0

0.5

0.0 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1.0

x

f(x) = (2 sin x)=x x = 1 ( 2)=8 = 0:125 x 2 1:875 1:75 1:625 1:5 1:375 1:25 1:125 1 f (x) 0:90 1:01 1:12 1:23 1:33 1:43 1:52 1:60 1:68 R 1 (2 sin x)=xdx t0:125(1:01+1:12+1:23+1:33+1:43+1:52+1:60+1:68) t 2 1:365 Valor con n=500 (2 sin x)=x Approximate integral (right boxes) is 1: 319 4 4. Integral de (2.sinx)/x entre -1 y -2 por regla del trapecio y n=8 (2 sin x)=x

2

2.0

y

1.51.0

0.5

0.0 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1.0

x

(x) = x=

2 sin x x

1

( 2)=8 = 0:125

x 2 1:875 1:75 1:625 1:5 1:375 1:25 1:125 1 f (x) 0:90 1:01 1:12 1:231:33 1:43 1:52 1:60 1:68 R 1 2 sin x 0:125 x dx t 2 (0:90 + 2(1:01) + 2(1:12) + 2(1:23) + 2(1:33) + 2(1:43) + 2 2(1:52) + 2(1:60) + 1:68) = 1: 316 3 Valor con n=500
2 sin x x

Approximate integral...