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Integration and solid of revolution

  1. Jun 16, 2008 #1
    hi i'm super stuck with this question:

    I'm super stuck with these two problems on one of my practice exams, can anyone help me out?

    Find the integral between 4 and 3 of (u^2 + 1) / (u - 2)^2

    and

    Find the volume of the solid of revolution obtained by rotating, a full turn about the x-axis, the area between the x-axis and the curve y = 2 sin x, for x ∈ [ π , 3π ].

    Thanks
    if anyone can help me out
     
  2. jcsd
  3. Jun 16, 2008 #2

    rock.freak667

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    Homework Helper

    Well for the first one


    [tex]\int _3 ^{4} \frac{u^2 + 1}{(u - 2)^2} du[/tex]


    consider the integrand alone


    [tex]\frac{u^2 + 1}{(u - 2)^2} \equiv \frac{u^2+1}{u^2-4u+4}[/tex]


    the degree of the polynomial in the numerator [itex] \geq[/itex] degree of the polynomial of the denommerator.

    You need to divide it out until the degree of the polynomial in the numerator < degree of the polynomial of the denominator.
     
  4. Jun 16, 2008 #3

    Defennder

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    For the second one just use the formula for evaluating the solid of revolution [tex]\pi \int^{3\pi}_{\pi} f(x)^2 dx[/tex]
     
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