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Math Help - Some tricky diff problems

  1. #1
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    Some tricky diff problems

    Hi I have a some problems I could use help working through, if anyone could help me out here Id be v greatful!!

    (1)

    <br />
\int {\frac{{dx}}<br />
{{\sqrt {4x^2  - 9} }}} <br />
    (hyperbolic function)

    (2)

    <br />
\oint\limits_r {\{ (x^2  - y)dx + (y^2  + x)dy\} } <br />

    Where r is the closed path, mapped counterclockwise, described by the square with verticies at (0,0),(1,0),(1,1),(0,1)



    (3)

    - use greens theorem to evaluate

    <br />
\oint\limits_r {\{ (y\exp [x^2 y^2 ] - y)dx + (x\exp [x^2 y^2 ] + x)dy\} } <br />

    where r, mapped counterclockwise, is the circle of th radius a with centre at the origin.
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  2. #2
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    \int \frac{dx}{\sqrt{4x^{2} - 9}}

    Recall that: \int \frac{dx}{\sqrt{x^{2} - a^{2}}} = \cosh^{-1} \left(\frac{x}{a}\right) + C

    So you have to factor out the 4 under the radical in the denominator so you can isolate it from the x^{2} in order to use the standard integral.
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  3. #3
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    For (2), can't you sum the integrals along each side of the square, since on any given side, either x or y is constant?
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  4. #4
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    Quote Originally Posted by sleepingcat View Post
    For (2), can't you sum the integrals along each side of the square, since on any given side, either x or y is constant?
    Yes.

    -Dan
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