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Cómo calcular la longitud de arco de una curva dada

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Cómo calcular la longitud de arco de una curva dada

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En este vídeo, se plasma el desarrollo para determinar la longitud de arco de una curva en R3, comprobando el resultado en Geogebra.

Created by

Yuridiana Lopez Arias
Yuridiana Lopez Arias
Mexico

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Cómo calcular la longitud de arco de una curva dada
 

Cómo calcular la longitud de arco de una curva dadaOnline version

En este vídeo, se plasma el desarrollo para determinar la longitud de arco de una curva en R3, comprobando el resultado en Geogebra.

by Yuridiana Lopez Arias
QR
1

Para describir la curva r(t) se le asignan valores a:

2

Los puntos P y Q se obtienen:

Selecciona una o varias respuestas

3

r'(t) indica:

4

La derivada de r(t)=(2*cos(t), (raíz cuadrada de 5)*t, 2*sen (t)) es:

5

La magnitud de un vector se refiere a :

6

La longitud de arco se calcula mediante:

7

La identidad trigonométrica que se usa para la simplificación es:

8

el resultado de la integral dt es:

9

El comando utilizado en Geogebra para plasmar la curva es:

10

Comando utilizado en Geogebra para comprobar el resultado del ejercicio:

Explicación

Al darlo un valor al parámetro "t" y sustituirlo en cada componente de la curva, nos dará los puntos coordenada, que al unirlos, plasmarán la curva de la función dada.

La pregunta se centra en recordar que el resultado de la integral cuando sólo aparece el diferencial es la variable misma. Es decir, en este caso, cuando se calcula la integral de "dt", se obtiene como resultado sólo "t" ( es como si se eliminara el diferencial con la integral). El "3" por ser constante, sale y se sigue llevando en la operación.

 
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