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AbdulRehman

find the volume enclosed by x²+y²=4 and z=x+4y using multiple integrals?

  • 2 years ago
  • 2 years ago

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  1. rim182946
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    I think you need more information like z = 0 ( so it can be above the xy plane )

    • 2 years ago
  2. AbdulRehman
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    Then find the area only in first ocatne

    • 2 years ago
  3. rim182946
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    \[\int\limits_{0}^{\pi/2}\int\limits_{0}^{2}\int\limits_{0}^{r \cos \theta+4r \sin \theta}rdzdrd \theta\]

    • 2 years ago
  4. rim182946
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    you should use cyindrical because the region in the xy plane is circular in nature you have to convert the z bounds then the low z bound is z = 0 and the high z bound is z = x + 4y you said only the first octant so after the z integration you are down to the quarter circle in the first quadrant which has r bounds r = 0 to r = 2 (the circle of radius 2 centered at the origin) theta bounds of theta = o to theta = Pi/2

    • 2 years ago
  5. AbdulRehman
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    Well that is quite right. I find difficulty in drawing graph in 3d through and then finding it's limit. Any guess.

    • 2 years ago
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