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kevin7ama

  • 2 years ago

im having trouble integrating the double iterated integral R= [0,3] X [0,rad(9-y^2)] and the function inside the integral is "y dy dx"

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  1. kevin7ama
    • 2 years ago
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    \[\int\limits_{0}^{3}\int\limits_{0}^{\sqrt{9-7^{2}}} y dy dx\] thats the integral

  2. Algebraic!
    • 2 years ago
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    something's not right with either your limits or your order of integration...

  3. kevin7ama
    • 2 years ago
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    sorry your right.... its y dx dy

  4. Algebraic!
    • 2 years ago
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    if you're integrating in 'dy' .. your limits will be functions of x

  5. Algebraic!
    • 2 years ago
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    ok

  6. Algebraic!
    • 2 years ago
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    that works...

  7. Algebraic!
    • 2 years ago
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    integral of ydx is yx +C

  8. kevin7ama
    • 2 years ago
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    ive tried u sub...and integration by parts. but i just cant get the answer....

  9. Algebraic!
    • 2 years ago
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    still something weird about it though... shouldn't be written like that...

  10. kevin7ama
    • 2 years ago
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    the problem just says.... evaluate the iterated integral

  11. Algebraic!
    • 2 years ago
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    k

  12. Algebraic!
    • 2 years ago
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    they're writing it weird to try and throw you off I guess...

  13. Algebraic!
    • 2 years ago
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    anyway... plug in the limits on 'x' ... ( 0 ... srt(9-y^2) ) and then evaluate with respect to dy

  14. kevin7ama
    • 2 years ago
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    but then what? dont we need to simplifly

  15. Algebraic!
    • 2 years ago
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    so (y*sqrt(9-y^2) + C) dy

  16. Algebraic!
    • 2 years ago
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    you can use u sub.s ...

  17. Algebraic!
    • 2 years ago
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    9-y^2 = u -2y dy = du y dy = -du/2

  18. kevin7ama
    • 2 years ago
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    yes but then we need to plug in 3 into \[\sqrt{9-3^{2}}\] wich equals 0 in the rad

  19. Algebraic!
    • 2 years ago
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    so?

  20. kevin7ama
    • 2 years ago
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    ends up canceling everything out.... and the answer is supposed to be 3

  21. Algebraic!
    • 2 years ago
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    ...

  22. Algebraic!
    • 2 years ago
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    lower limit?

  23. kevin7ama
    • 2 years ago
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    is 0

  24. kevin7ama
    • 2 years ago
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    omg....

  25. kevin7ama
    • 2 years ago
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    ive done this problem like no lie 10 times and i never pluged in the lower limit = 0 giving me the right answer 9

  26. kevin7ama
    • 2 years ago
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    thank you so much for letting me realize this. how to i give a medal??

  27. Algebraic!
    • 2 years ago
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    click 'best response'

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