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Calcular volumen, ...

efp Ver Perfil del Miembro Ver los mensajes de este miembro	Oct 12 2010, 05:44 PM Publicado: #1
Matemático Grupo: Usuario FMAT Mensajes: 34 Registrado: 21-January 10 Desde: Mexico Miembro Nº: 65.274 Nacionalidad: Sexo:	Calcular el volumen encerrado por: $TEX: $cb^{2}x^{2}+ca^{2}y^{2}=a^{2}b^{2}z$, $c>0$ y el plano $z=h, \ h>0$$ -------------------- La Perfecta Fluctuación del Universo "The secret side of me I never let you see I keep it caged But I can't control it So stay away from me The beast is ugly I feel the rage And I just can't hold it It's scratching on the walls In the closet, in the halls It comes awake And I can't control it Hiding under the bed In my body, in my head Why won't somebody come and save me from this? Make it end! I feel it deep within, It's just beneath the skin I must confess that I Feel like a monster I hate what I've become The nightmare's just begun I must confess that I Feel like a monster I feel like a monster My secret side I keep Hid under lock and key I keep it caged But I can't control it Cause if I let him out He'll tear me up And break me down Why won't somebody come and save me from this? Make it end! I feel it deep within, It's just beneath the skin I must confess that I Feel like a monster I hate what I've become The nightmare's just begun I must confess that I Feel like a monster I feel like a monster It's hiding in the dark It's teeth are razor sharp There's no escape for me It wants my soul, It wants my heart No one can hear me scream Maybe it's just a dream Or maybe it's inside of me Stop this monster! I feel it deep within, It's just beneath the skin I must confess that I Feel like a monster I hate what I've become The nightmare's just begun I must confess that I Feel like a monster I feel like a monster"

Laðeralus Ver Perfil del Miembro Ver los mensajes de este miembro	Nov 22 2010, 08:12 PM Publicado: #2
Dios Matemático Supremo Grupo: Usuario FMAT Mensajes: 947 Registrado: 28-September 07 Desde: Santiago Miembro Nº: 10.639 Nacionalidad: Universidad: Sexo:	$TEX: <br />Solución con integrales triples. La primera superficie corresponde a un paraboloide elíptico (paraboloide circular si $a=b$, y ambos diferentes de cero, sino no tendría sentido). La segunda superficie es un plano horizontal con respecto al plano xy, y de altura $h$, con $h>0$. \\<br /><br />Se realiza el siguiente cambio de variables:<br />\[ T(x;y;z) = \left( \frac{a}{\sqrt{c}} r \cos(\theta) ; \frac{b}{\sqrt{c}} r \sin(\theta) ; z \right)\]<br /><br />Su Jacobiano está dado por $J =\frac{ab}{c} r $. Luego, $\| J \| = \frac{ \| ab \|}{c} r$. \\<br /><br />La transformación del paraboloide elíptico es $z = r^2$. La transformación del plano es $z=h$. La intersección de ambas es $r = \sqrt{h}$. Por lo tanto, los límites de integración son $0 \leq r \leq \sqrt{h} , 0 \leq \theta \leq 2\pi , r^2 \leq z \leq h$. \hspace{2mm}\\<br /><br />Finalmente, el volumen queda expresado por:<br /><br />\[ V = \int_{0}^{2\pi} \int_{0}^{\sqrt{h}} \int_{r^2}^{h} \frac{\| ab\|}{c} r dz dr d\theta \]<br />\[ V = \left(2\pi\right) \left( \frac{\| ab\|}{c} \right) \int_{0}^{\sqrt{h}} r(h-r^2) dr \]<br />\[ V = \frac{ \pi \|ab \| h^2}{2c} \]<br /><br />$

efp Ver Perfil del Miembro Ver los mensajes de este miembro	Nov 23 2010, 07:16 PM Publicado: #3
Matemático Grupo: Usuario FMAT Mensajes: 34 Registrado: 21-January 10 Desde: Mexico Miembro Nº: 65.274 Nacionalidad: Sexo:	La respuesta se ve bien... Ahora a esperar otra respuesta mediante una integral simple... Saludos... -------------------- La Perfecta Fluctuación del Universo "The secret side of me I never let you see I keep it caged But I can't control it So stay away from me The beast is ugly I feel the rage And I just can't hold it It's scratching on the walls In the closet, in the halls It comes awake And I can't control it Hiding under the bed In my body, in my head Why won't somebody come and save me from this? Make it end! I feel it deep within, It's just beneath the skin I must confess that I Feel like a monster I hate what I've become The nightmare's just begun I must confess that I Feel like a monster I feel like a monster My secret side I keep Hid under lock and key I keep it caged But I can't control it Cause if I let him out He'll tear me up And break me down Why won't somebody come and save me from this? Make it end! I feel it deep within, It's just beneath the skin I must confess that I Feel like a monster I hate what I've become The nightmare's just begun I must confess that I Feel like a monster I feel like a monster It's hiding in the dark It's teeth are razor sharp There's no escape for me It wants my soul, It wants my heart No one can hear me scream Maybe it's just a dream Or maybe it's inside of me Stop this monster! I feel it deep within, It's just beneath the skin I must confess that I Feel like a monster I hate what I've become The nightmare's just begun I must confess that I Feel like a monster I feel like a monster"

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