Taller de Cálculo Vectorial - 3er Corte
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Naomi Ávila - Salomé Oñate Cálculo Vectorial, Grupo A2 1. ∫ C ❑ x 2 +y 2 +z 2 ds c { c 1 : ⟨ 2cos t, 0 , 2sin t ⟩ ; 0 ≤t≤ π 2 c 2 : ⟨ 0 ,t, 2− 2 t ⟩ ; 0 ≤t≤ 1 c 3 : ⟨ t, 1−t, 0 ⟩ ; 0 ≤t≤ 1 } Para C 1 : V ( t ) =⟨ −2sin t, 0 , 2cos t ⟩ |V ( t) | = √ ( −2sin t ) 2 +( 0 ) 2 +( 2cos t ) 2 = √ 4 ( cos 2 t+sin 2 t ) =2 F ( f ( t) ,g ( t) ,h ( t) )=( 2cos t ) 2 +( 0 ) 2 + ( 2sin t ) 2 =4 ( cos 2 t+ sin 2 t) =4 ∫ 0 π 2 ( 4)( 2) dt= 8 ( π 2 ) =4 π Para C 2 : V ( t ) =⟨ 0 , 1 ,−2 ⟩ |V ( t) | = √ ( 0) 2 +( 1) 2 +( −2) 2 =√ 5 F ( f ( t) ,g ( t) ,h ( t) )=( 0 ) 2 + ( t ) 2 +( 2− 2 t) 2 =t 2 +4−8 t+ 4 t 2 =5 t 2 −8 t +4 ∫ 0 1 ( 5 t 2 −8 t+ 4 ) ( √ 5 ) dt=( √ 5 ) ( 5 t 3 3 −4 t 2 + 4 t ) = 5 √ 5 3 Para C 3 : V ( t ) =⟨ 1 ,−1 , 0 ⟩ |V ( t) | = √ ( 1) 2 +( −1) 2 +( 0) 2 =√ 2 F ( f ( t) ,g ( t) ,h ( t) )=( t ) 2 + ( 1−t) 2 +( 0) 2 =2 t 2 −2 t+1
description
Calculo de Multivariable
Transcript of Taller de Cálculo Vectorial - 3er Corte
Naomi vila - Salom Oate
Clculo Vectorial, Grupo A2
1.
Para :
Para :
Para :
GRAFICA 1.
clc
close all
clear all
axis([-1 4 -1 4 -1 4])
line([-1 4],[0 0],[0 0],'color','k')
line([0 0],[-1 4],[0 0],'color','k')
line([0 0],[0 0],[-1 4],'color','k')
grid on
hold on
%curva C1
t=0:0.01:1/2*pi;
x=2*cos(t);
y=0*t;
z=2*sin(t);
plot3(x,y,z,'b')
%curva C2
t=0:0.1:1;
x=0*t;
y=t;
z=2-2*t;
plot3(x,y,z,'g')
%curva C3
t=0:0.1:1;
x=t;
y=1-t;
z=0*t;
plot3(x,y,z,'r')
2. ; ;
GRAFICA 2.
clc
close all
clear all
axis([-1 4 -1 4 -1 4])
line([-1 4],[0 0],[0 0],'color','k')
line([0 0],[-1 4],[0 0],'color','k')
line([0 0],[0 0],[-1 4],'color','k')
grid on
hold on
t=0:0.01:2*pi;
x=t.*cos(t);
y=t.*sin(t);
z=t;
plot3(x,y,z,'g')
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Para :
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Para :
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Para :
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GRAFICA 3.
clc
close all
clear all
axis([-1 2 -1 2 ])
line([-1 2],[0 0],'color','k')
line([0 0],[-1 2],'color','k')
grid on
hold on
% LADO 1
t=0:0.01:1;
x=t;
y=0*t;
plot(x,y,'y')
% LADO 2
t=0:0.01:1;
x=1-t;
y=t;
plot(x,y,'r')
% LADO 3
t=0:0.01:1;
x=0*t;
y=1-t;
plot(x,y,'g')
4. ; ;
;
=
GRAFICA 4.
clc
close all
clear all
axis([-1 4 -1 4 ])
line([-1 4],[0 0],'color','k')
line([0 0],[-1 4],'color','k')
grid on
t=1/4*pi:0.01:1/2*pi;
x=2*cos(t);
y=2*sin(t);
plot(x,y,'g')
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