Necesito ayuda con estos ejercicios de integral?
Necesito ayuda con estos ejercicios de integral.
2Estradaarzola
En resumen
(b) D = {(x, y, z) : 0 ≤ x ≤ 1 , 0≤ y ≤ 1 - x , 0 ≤ z ≤ 1 - x - y} <img src="https://tex.z-dn.net/?
Mejor respuesta
DerGhost2538
(b) D = {(x, y, z) : 0 ≤ x ≤ 1 , 0≤ y ≤ 1 - x , 0 ≤ z ≤ 1 - x - y}
<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AI%3D%5Ciiint%5Climits_%7BD%7D%281%2Bx%2By%2Bz%29%5E%7B-3%7DdV%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cint_%7B0%7D%5E%7B1%7D%5Cint_%7B0%7D%5E%7B1-x%7D%5Cint_%7B0%7D%5E%7B1-x-y%7D%281%2Bx%2By%2Bz%29%5E%7B-3%7D~dz~dy~dx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cint_%7B0%7D%5E%7B1%7D%5Cint_%7B0%7D%5E%7B1-x%7D-%5Cdfrac%7B1%7D%7B4%7D%20%5Cleft.%281%2Bx%2By%2Bz%29%5E%7B-4%7D%5Cright%7C_%7Bz%3D0%7D%5E%7Bz%3D1-x-y%7D~dy~dx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D-%5Cdfrac%7B1%7D%7B4%7D%20%5Cint_%7B0%7D%5E%7B1%7D%5Cint_%7B0%7D%5E%7B1-x%7D%5Cdfrac%7B1%7D%7B16%7D-%281%2Bx%2By%29%5E%7B-4%7D~dy~dx%0A" />
<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AI%3D-%5Cdfrac%7B1%7D%7B4%7D%20%5Cint_%7B0%7D%5E%7B1%7D%5Cleft.%5Cleft%5B%5Cdfrac%7By%7D%7B16%7D-%5Cdfrac%7B%281%2Bx%2By%29%5E%7B-5%7D%7D%7B-5%7D%5Cright%5D%5Cright%7C_%7By%3D0%7D%5E%7By%3D1-x%7D~dx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D-%5Cdfrac%7B1%7D%7B4%7D%20%5Cint_%7B0%7D%5E%7B1%7D%5Cdfrac%7B1-x%7D%7B16%7D%2B%5Cdfrac%7B1%7D%7B160%7D%20-%5Cdfrac%7B%281%2Bx%29%5E%7B-5%7D%7D%7B5%7D~dx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D-%5Cdfrac%7B1%7D%7B640%7D%20%5Cint_%7B0%7D%5E%7B1%7D11-10x-32%281%2Bx%29%5E%7B-5%7D~dx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D-%5Cdfrac%7B1%7D%7B640%7D%20%5Cleft.%5Cleft%5B11x-5x%5E2%2B%5Cdfrac%7B32%7D%7B6%7D%281%2Bx%29%5E%7B-6%7D%5Cright%5D%5Cright%7C_%7Bx%3D0%7D%5E%7Bx%3D1%7D%5C%5C%20%5C%5C%20%5C%5C%0AI%3D-%5Cdfrac%7B1%7D%7B640%7D%5Cleft%2811-5%2B%5Cdfrac%7B16%7D%7B3%7D%5Ctimes2%5E%7B-6%7D-%5Cdfrac%7B16%7D%7B3%7D%5Cright%29%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cdfrac%7B3%7D%7B128%7D" /> = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
(c) D = {(x, y, z) : 0 ≤ x≤ 1 , 0 ≤ y ≤ 1 - x , 0 ≤ z ≤ x² + y²}
<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AI%3D%5Ciiint%5Climits_%7BD%7DdV%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cint_%7B0%7D%5E%7B1%7D%5Cint_%7B0%7D%5E%7B1-x%7D%5Cint_%7B0%7D%5E%7Bx%5E2%2By%5E2%7Ddz~dy~dx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cint_%7B0%7D%5E%7B1%7D%5Cint_%7B0%7D%5E%7B1-x%7Dx%5E2%2By%5E2~dy~dx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cint_%7B0%7D%5E%7B1%7D%20%5Cleft.%5Cleft%28x%5E2y%2B%5Cdfrac%7By%5E3%7D%7B3%7D%5Cright%29%5Cright%7C_%7By%3D0%7D%5E%7By%3D1-x%7Ddx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cint_%7B0%7D%5E%7B1%7D%20x%5E2%281-x%29%2B%5Cdfrac%7B%281-x%29%5E3%7D%7B3%7D~dx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cint_%7B0%7D%5E%7B1%7D%20x%5E2-x%5E3%2B%5Cdfrac%7B%281-x%29%5E3%7D%7B3%7D~dx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cleft.%5Cleft%5B%5Cdfrac%7Bx%5E3%7D%7B3%7D-%5Cdfrac%7Bx%5E4%7D%7B4%7D-%5Cdfrac%7B%281-x%29%5E4%7D%7B12%7D%5Cright%5D%5Cright%7C_%7B0%7D%5E%7B1%7D%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cdfrac%7B1%7D%7B3%7D-%5Cdfrac%7B1%7D%7B4%7D%2B%5Cdfrac%7B1%7D%7B12%7D%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cdfrac%7B1%7D%7B6%7D%0A" />.