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Math Help - Multiple Integrals

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    Multiple Integrals

    Thanks for the help!

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  2. #2
    Senior Member DeMath's Avatar
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    Quote Originally Posted by qbkr21 View Post
    Thanks for the help!

    z = 2 + y,{\text{ }}z = 3y.

    2 + y = 3y \Leftrightarrow y = 1.

    y = {x^2} = 1 \Leftrightarrow x =  \pm 1.

    So D = \left\{ {\left( {x,y} \right):{\text{ }}{x^2} \leqslant y \leqslant 1,{\text{ }} - 1 \leqslant x \leqslant 1} \right\}.

    V = \iint\limits_D {\left( {2 + y} \right)dydx} - \iint\limits_D {3ydydx} = 2\iint\limits_D {\left( {1 - y} \right)dydx} =

    = 2\int\limits_{ - 1}^1 {\int\limits_{{x^2}}^1 {\left( {1 - y} \right)dydx} }  =  \ldots  = \frac{{16}}{{15}}.
    Last edited by DeMath; April 5th 2009 at 02:58 PM. Reason: typos
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    RE:

    Great I got the same answer. I thank you fine sir for the help!
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