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mathstina

  • 2 years ago

Evaluate the integral ∭(xz+3z)dV,where E is the region bounded by the cylinder x^2 +z^2 = 9 and the planes x+y=3,z=0 and y=0 above the xy-plane.

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  1. snaef999
    • 2 years ago
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    Im just donig these myself so I dont know how much help I can be, but the tricky part is setting up the limits in the correct order. I think the first limit is x + y = 3 so it would be -3 to 3 for the first one (I think)

  2. mathstina
    • 2 years ago
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    is it z-simple?

  3. mathstina
    • 2 years ago
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    hw?

  4. experimentX
    • 2 years ago
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    could you start by drawing picture?

  5. mathstina
    • 2 years ago
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    thats e part i confused abt. the region ...

  6. mathstina
    • 2 years ago
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    any help

  7. experimentX
    • 2 years ago
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    |dw:1353429220967:dw| draw your cylinder first

  8. experimentX
    • 2 years ago
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    draw your planes |dw:1353429469502:dw|

  9. experimentX
    • 2 years ago
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    |dw:1353429578503:dw| this is your last plane ... show how is the region gonna look like?

  10. mathstina
    • 2 years ago
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    ok. hw to find the limits?

  11. experimentX
    • 2 years ago
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    lol ... first of all picture your region ... then you will find the limits.

  12. experimentX
    • 2 years ago
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    |dw:1353430085406:dw|

  13. mathstina
    • 2 years ago
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    ok. then... i m nt strong in this chpt.

  14. experimentX
    • 2 years ago
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    first you need to visualize ... then approach the problem. |dw:1353430430927:dw|

  15. mathstina
    • 2 years ago
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    ok

  16. experimentX
    • 2 years ago
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    |dw:1353430738439:dw|

  17. experimentX
    • 2 years ago
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    |dw:1353430950975:dw|

  18. mathstina
    • 2 years ago
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    ok so far i unerstand. thanks . i need ur continual assistance; steps to e solution. i need to sign out. cya.

  19. experimentX
    • 2 years ago
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    |dw:1353431171488:dw|

  20. experimentX
    • 2 years ago
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    |dw:1353431242707:dw||dw:1353431281194:dw|

  21. mathstina
    • 2 years ago
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    if possible only could write the steps of the integration and the final ans.

  22. experimentX
    • 2 years ago
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    do you have final answer?

  23. experimentX
    • 2 years ago
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    from wolf i got around 64.8 http://www.wolframalpha.com/input/?i=Integration[Integration[Integration[xz%2B3z%2C+{y%2C+0%2C+3-x}]%2C+{z%2C+0%2C+sqrt%289+-+x^2%29}]%2C+{x%2C+0%2C+3}]

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