En este resumen vas a encontrar explicaciones, propiedades, teoremas, ejemplos de ejercicios resueltos y respuesta a ejercicios de libro "Lecciones de Análisis II" de Alfredo Novelli.
Tema: volúmenes de rotación (respecto al eje x, respecto al eje y)
Recordemos:
Sea rectanguloide del plano , de base , relativo a una función continua ( ) ≥ 0, haciendo
girar alrededor del eje obtenemos un sólido, llamado sólido de rotación, cuyo volumen es:
= ( )
( )= 2 = ( ) = 2 =
( ) ( )
Ahora bien, , entonces
2
( )
, de lo que se deduce que
=2
En el caso que gire una un dominio normal con respecto al eje :
( ) ( )
= ( )−" ( ) = # 2 % =2
$( ) $( )
Entonces
=2
&
, De igual manera se deduce la fórmula para el cálculo del volumen de rotación con respecto al eje :
' =2
&
Ejemplo: Calcular el volumen del sólido generado por la rotación, alrededor del eje
eje , del dominio plano ( = )( , ): 1 ≤ ≤0 1
y alrededor del
≤ log , 0 ≤
Vamos a calcular primero :
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller PuntoIngenieria. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.75. You're not tied to anything after your purchase.
