integrales dobles para hallar volumen

Cálculo de volúmenes mediante integrales doblesEn el primer tema dijimos que las integrales dobles pueden representar volúmenes. Imagina que queremos el volumen entre la función [color=rgba(0, 0, 0, 0)][/color]f(x,y) y el plano x,y[br]dentro del rectángulo R[br], como en la siguiente figura:[br][br][img]https://lh5.googleusercontent.com/CclMfc6W8Kg1iU5rWpkmsYy2OCzkR1TR6BzRGr0IsTXKzs-ij86KfFFgwHW8cWYx9DphH0hYo_C56seiy7MtlbI0yNZxvKS83GxkTUSvFPuoz8gwx0q0Hvnd2u5YvCymHRg7aqrr[/img][br][br][br] [br][br][br][img]data:image/png;base64,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[/img]V=[br][img]https://lh3.googleusercontent.com/FGg68Qf1u2oAhbF4q3aaUIPatWTV4DSopAf7bEZK6cOH5pPTFaoR7aldRZ-oILVNJM8JF0ReYeTylk2WR0MTpxujXLRDIDRIYVqYZQZXHfv9d3rxK8-VdqFih_aJMM8Jc0SjDhju[/img][br]Podemos reescribir el último plano como f(x,y)=z=1−x−y[br][br]y pensar que queremos el volumen entre la superficie del plano [br]inclinado y la región del plano xy      formada por el siguiente triángulo: [img]https://lh5.googleusercontent.com/T6fmuk-qU0LOWGWeuZXAx00msLo7fAp6AT0yb6sg2Cxt2McgNhWs30cwmdmQkYuowDj8zwyrZk6w23aQAPRMyckwgbIl83CRZJRsZJVv7ciWAoE8uItOkZDJjoEmcGbfLZ0f9Dxw[/img][br][br][br][br][br]¿Cómo obtuvimos ese triángulo? A través del gráfico vemos que el dominio es limitado por los ejes cartesianos y por la intersección del plano [color=rgba(0, 0, 0, 0)][/color]x+y+z= con el plano  xy[br], es decir, por la recta x+y=1 Entonces, f(x,y)=1−x−y representa la “altura” de la región en cada punto y dA representa el área sobre dicha altura. Llamando a esa región plana como [color=rgba(0, 0, 0, 0)][/color]D tenemos que: V=∬Df(x,y)dA=∬D(1−x−y)dx dy[br] Es decir, el volumen que queremos es la integral de la función que representa el plano inclinado en la región plana que trazamos anteriormente. Por tanto, necesitamos escribir matemáticamente a la región D como siempre hicimos en las integrales dobles. Como mencionamos, para descubrir la ecuación de la recta inclinada hacemos la intersección del plano z=1−x−ycon z=0, lo que nos da: 0=1−x−y[br] y=1−x[br][br] Escribiendo la región plana como tipo I, tenemos que y está entre las rectas y=0[br] y y=1−x, mientras que x[br] está entre x=0 y x=1 Por tanto, 0≤y≤1−x,0≤x≤1[br]. Llevándolo a la integral: V=∫10∫1−x0(1−x−y)dy dx[br][br] ¡Y resolvemos! Veamos un ejemplo un poco más complejo. Calculemos el volumen de la región limitada por los paraboloides z=x2+y2[br] y z=4−x2−y2. La región es esta:[img]https://lh6.googleusercontent.com/rgljkYsKwJYynTnyJUofHkNqKS8Ilr9TPp4RhqlBqfh5WQ1FP8vQnJ5qfLyFk58ph3soSd-fL5GSV4ippEtrfRaHqFLKs6r2ftpjkatw5pS2Y66nsPgZ2YOJCRMz-1GUhe0xctnP[/img] Podemos pensar que está limitada por las dos funciones f(x,y)=z=x2+y2 y g(x,y)=z=4−x2−y2[br] ¿La “altura” de esa región no siempre será z del paraboloide naranja del paraboloide naranja−−z del paraboloide azul del paraboloide azul? Es decir, esa “altura” es g(x,y)−f(x,y)[br] Bien, si para hallar el volumen de la región, tenemos que integrar una altura en un área, solo decimos que V=∬Dg(x,y)−f(x,y)dA[br][br] V=∬D(4−x2−y2)−(x2+y2)dA=∬D(4−2x2−2y2)dA[br][br] Donde D[br] es el área que limita el volumen en el plano xy (la proyección del volumen):
[img]https://lh5.googleusercontent.com/8BkDbIrKXqK8eR6GOhjbqJ0DPPDbQT_OqFdKyhPVLr5OQaBFZqMAF0vzHdtZF7cdK73Je_9So-ln9ExISCNhi7q9UATmYTSlmGjZ6-5CNCO4HFknKScI9mfLYnNZCr1-AZDhfwfV[/img] Escribimos la región D como en cualquier integral doble. Como es un círculo, utilizamos coordenadas polares. x=rcosθ[br] y=rsenθ[br] J=r[br] El círculo es definido como 0≤r≤2√ y 0≤θ≤2π[br] El límite 2√2 del radio puede ser encontrado haciendo la intersección entre los paraboloides: z=x2+y2=4−x2−y2[br] x2+y2=2[br] Llevándolo a la integral, tenemos: V=∬D(4−2x2−2y2)dA=2∫2π0∫2√0(2−r2)rdrdθ[br] ¡Y resolvemos!  Entonces, la finalidad de este capítulo es entender cómo escribir el volumen mediante una integral doble (identificando quién es la “altura” y quién es el “área” que la limita en el plano).

Information: integrales dobles para hallar volumen