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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)

  • 2 years ago
  • 2 years 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) ?

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

    • 2 years ago
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    yes

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

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

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

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

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

    • 2 years 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|

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

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

    • 2 years ago
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    congrads!

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

    • 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.

    • 2 years ago
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    terms of y*

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

    • 2 years ago
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    |dw:1352139848664:dw|

    • 2 years ago
  18. psk981 Group Title
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    how so

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

    • 2 years ago
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    so that should be the inner bound

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

    • 2 years ago
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    yes

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

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

    • 2 years ago
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