1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Did you have a question?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook