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Math Help - urgent help for calc 3

  1. #1
    Junior Member
    Joined
    Aug 2007
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    71

    urgent help for calc 3

    I don't get the first integral. How do they get to x(sqrt(x^2 + ^2 +1)? I would think you would need a ln.
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  2. #2
    Junior Member
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    Aug 2007
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    shouldn't there be a 0.5(x(....) for the first integral?
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  3. #3
    Senior Member
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    The 0.5 gets cancelled out when you divide by the new power of 1/2.
    <br />
\int \frac{xy}{\sqrt{x^2+y^2+1}}dy

    u = x^2+y^2+1
    du = 2ydy
    <br />
\int \frac {1}{2}x \frac {2ydy}{\sqrt{u}}
    =\int \frac{1}{2}xu^{-1/2}du
    =\frac {1}{2}x2u^{1/2}
    x\sqrt{x^2+y^2+1}
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