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Homework Help: Trigonometric substitution

  1. Mar 21, 2010 #1
    [tex]
    9x^2-4y^2=36
    [/tex]
    [tex]
    \frac{x^2}{4}-\frac{y^2}{9}=1
    [/tex]
    [tex]
    y=\frac{3}{2}\sqrt{x^2-4}
    [/tex]
    [tex]
    3\int_{2}^{3}\sqrt{x^2-4}dx
    [/tex]
    [tex]
    x=2sect
    [/tex]
    [tex]
    dx=2secttant
    [/tex]
    [tex]
    12\int_{a}^{b}tan^2tsectdt
    [/tex]
    [tex]
    12\int_{a}^{b}(sec^2t-1)(sect)dt
    [/tex]
    [tex]
    12\int sec^3tdt-12\int sectdt
    [/tex]
    [tex]
    6\int secttant-6\int ln|sect+tant|
    [/tex]
    [tex]
    sect=\frac{x}{2}
    [/tex]
    [tex]
    tant=\frac{\sqrt{x^2-4}}{2}
    [/tex]
    [tex]
    \frac{3x\sqrt{x^2-4}}{2}-6ln|\frac{x+\sqrt{x^2-4}}{2}| [2,3]
    [/tex]
    [tex]
    \frac{9\sqrt{5}}{2}-6ln|3+\sqrt{5}|+C
    [/tex]
     
  2. jcsd
  3. Mar 21, 2010 #2

    vela

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