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psk981 Group Title

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

  • one year ago
  • one year ago

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  1. TuringTest Group Title
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    draw the region, what is the equation of the line between (1,0) and (0,1) ?

    • one year ago
  2. psk981 Group Title
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    |dw:1352136497588:dw|

    • one year ago
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    yes

    • one year ago
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    only reversed, gotta have the constant last or you won't get a constant as an answer!

    • one year ago
  5. psk981 Group Title
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    how would my integrals look

    • one year ago
  6. TuringTest Group Title
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    the inner integral is bounded by the function -x, the outer by the constants

    • one year ago
  7. psk981 Group Title
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    after i solve it i get 2/3

    • one year ago
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    I get 3/4 can you show your work?

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

    • one year ago
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    |dw:1352137394567:dw|you dropped the /2 part...

    • one year ago
  11. psk981 Group Title
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    ok sweet i got it

    • one year ago
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    congrads!

    • one year ago
  13. psk981 Group Title
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    but order doesn't matter if you have constants

    • one year 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.

    • one year ago
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    terms of y*

    • one year ago
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    @psk981 I just realized we messed this one up :P

    • one year ago
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    |dw:1352139848664:dw|

    • one year ago
  18. psk981 Group Title
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    how so

    • one year ago
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    this function ain't -x, it's 1-x|dw:1352139902007:dw|

    • one year ago
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    so that should be the inner bound

    • one year ago
  21. psk981 Group Title
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    so goes from 0 to 1-x

    • one year ago
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    yes

    • one year ago
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    and|dw:1352140168346:dw|so I totally space out on the last one, sorry

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

    • one year ago
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