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Determine intervals of integration

asked 2015-02-05 15:04:59 +0200

sztike93 gravatar image

updated 2015-02-08 10:33:07 +0200

FrédéricC gravatar image

I have the following set: A = {(x,y)|x>=0, y>=0, x^2+y^2 <= 1} and I am required to compute the integral over A of y according to x and y (dxdy). How can I determine the interval to integrate on?

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answered 2015-02-05 17:42:23 +0200

rws gravatar image

Homework? I would not solve it with Sage but graphically: which geometric objects do the three relations represent?

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quadrant of a unit circle, so at first thought, both x and y should be between 0 and 1, but then, there's this constraint that x^2+y^2 <= 1, and I don't know how to use this information.

sztike93 gravatar imagesztike93 ( 2015-02-05 17:43:18 +0200 )edit

You should prove that y can be bounded by a well defined function of x !

tmonteil gravatar imagetmonteil ( 2015-02-05 17:48:50 +0200 )edit

hmm. So, you're saying that I should integrate from 0 to 1 and from -sqrt(1-x^2) to sqrt(1-x^2) y according to y and x (dydx)?

sztike93 gravatar imagesztike93 ( 2015-02-05 17:52:04 +0200 )edit

Almost ! Note that y is nonnegative. Drawing a picture may help.

tmonteil gravatar imagetmonteil ( 2015-02-06 23:29:47 +0200 )edit

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Asked: 2015-02-05 15:04:59 +0200

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Last updated: Feb 06 '15