psk981
integrate f(x,y)= x^2 +y over a triangular region bounded by (0,0), (1,0),(0,1)
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TuringTest
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draw the region, what is the equation of the line between (1,0) and (0,1) ?
psk981
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|dw:1352136497588:dw|
TuringTest
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yes
TuringTest
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only reversed, gotta have the constant last or you won't get a constant as an answer!
psk981
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how would my integrals look
TuringTest
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the inner integral is bounded by the function -x, the outer by the constants
psk981
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after i solve it i get 2/3
TuringTest
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I get 3/4
can you show your work?
psk981
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\[\int\limits_{0}^{1} \int\limits_{0}^{-x} x^{2}+y dydx \]
|dw:1352137141341:dw|
|dw:1352137253709:dw|
TuringTest
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|dw:1352137394567:dw|you dropped the /2 part...
psk981
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ok sweet i got it
TuringTest
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congrads!
psk981
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but order doesn't matter if you have constants
TuringTest
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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.
TuringTest
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terms of y*
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@psk981 I just realized we messed this one up :P
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|dw:1352139848664:dw|
psk981
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how so
TuringTest
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this function ain't -x, it's 1-x|dw:1352139902007:dw|
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so that should be the inner bound
psk981
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so goes from 0 to 1-x
TuringTest
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yes
TuringTest
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and|dw:1352140168346:dw|so I totally space out on the last one, sorry
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\[\int_0^1\int_0^{1-x}x^2+ydydx=\int_0^1\left.x^2y+\frac{y^2}2\right|_0^{1-x}dx\]