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psk981

  • 2 years ago

integrate f(x,y)= x^2 +y over a triangular region bounded by (0,0), (1,0),(0,1)

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  1. TuringTest
    • 2 years ago
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    draw the region, what is the equation of the line between (1,0) and (0,1) ?

  2. psk981
    • 2 years ago
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    |dw:1352136497588:dw|

  3. TuringTest
    • 2 years ago
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    yes

  4. TuringTest
    • 2 years ago
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    only reversed, gotta have the constant last or you won't get a constant as an answer!

  5. psk981
    • 2 years ago
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    how would my integrals look

  6. TuringTest
    • 2 years ago
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    the inner integral is bounded by the function -x, the outer by the constants

  7. psk981
    • 2 years ago
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    after i solve it i get 2/3

  8. TuringTest
    • 2 years ago
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    I get 3/4 can you show your work?

  9. psk981
    • 2 years ago
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    \[\int\limits_{0}^{1} \int\limits_{0}^{-x} x^{2}+y dydx \] |dw:1352137141341:dw| |dw:1352137253709:dw|

  10. TuringTest
    • 2 years ago
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    |dw:1352137394567:dw|you dropped the /2 part...

  11. psk981
    • 2 years ago
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    ok sweet i got it

  12. TuringTest
    • 2 years ago
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    congrads!

  13. psk981
    • 2 years ago
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    but order doesn't matter if you have constants

  14. TuringTest
    • 2 years ago
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    If both bounds are constants then often not, but sometimes the integral is only possible in a certain order. In this case we have the bounds as one constant, and one function. You could have done this one in the other order, but you would have to change the inner function to terms of yu.

  15. TuringTest
    • 2 years ago
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    terms of y*

  16. TuringTest
    • 2 years ago
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    @psk981 I just realized we messed this one up :P

  17. TuringTest
    • 2 years ago
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    |dw:1352139848664:dw|

  18. psk981
    • 2 years ago
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    how so

  19. TuringTest
    • 2 years ago
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    this function ain't -x, it's 1-x|dw:1352139902007:dw|

  20. TuringTest
    • 2 years ago
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    so that should be the inner bound

  21. psk981
    • 2 years ago
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    so goes from 0 to 1-x

  22. TuringTest
    • 2 years ago
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    yes

  23. TuringTest
    • 2 years ago
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    and|dw:1352140168346:dw|so I totally space out on the last one, sorry

  24. TuringTest
    • 2 years ago
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    \[\int_0^1\int_0^{1-x}x^2+ydydx=\int_0^1\left.x^2y+\frac{y^2}2\right|_0^{1-x}dx\]

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