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: Area bounded by these lines and curves

  1. May 5, 2006 #1
    Find the area of a figure bounded by the equilateral hyperbola [itex]xy = a^2[/itex], the x-axis, and the lines [itex]x = a[/itex], [itex]b = 2a[/itex].

    My work:
    The equations of the lines and curves involved here are:
    [tex]xy = a^2[/tex]
    [tex]y = 0[/tex]
    [tex]x = a[/tex]
    I don't know how b=2a is treated as an equation of a line here & hence I am puzzled as how to get the limits for the definite integral here. Well the formula I tried using is(Q stands for area):
    [tex]Q = \int_a^b [f_1(x) - f_2(x)]dx[/tex]

    Guidance needed.
     
  2. jcsd
  3. May 5, 2006 #2
    I guess it's a typo. It's probably x = 2a.
     
  4. May 6, 2006 #3
    Thanks, you are right! :smile:
    [tex]y = {a^2\over x} [/tex]
    [tex]Q = \int_a^{2a} {a^2\over x} = a^2\ln 2[/tex]

    ...which tallies with the solution given :biggrin:.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook