Results 1 to 4 of 4

Math Help - How do you calculate the area under hyperbola?is this correct? what do I do next?

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    13

    How do you calculate the area under hyperbola?is this correct? what do I do next?

    How do you calculate the area under hyperbola?is this correct? what do I do next?-math.jpg

    I found y = \sqrt{\frac{b^2x^2}{a^2} - b^2}

    then Area = b \int \sqrt{\frac{x^2}{a^2} - 1}dx with upper limit c and lower a.

    I then let x = acosht, is this correct?

    then did the method of substitution.

    then what do I do? My end answer looks very weird...so i just want to make sure.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Aug 2008
    Posts
    903
    Solve it parametrically if we know that the parametric representation of the right side of a hyperbola \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 is given by x=a\cosh(t), y=b\sinh(t). So then the area is:

    \int_a^c ydx=\int_{t_0}^{t_1} y(t) d(x(t))=\int_{t_0}^{t_1} b\sinh(t) a\sinh(t)dt.

    You can find the limits in terms of t right?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2010
    Posts
    13
    Quote Originally Posted by shawsend View Post
    Solve it parametrically if we know that the parametric representation of the right side of a hyperbola \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 is given by x=a\cosh(t), y=b\sinh(t). So then the area is:

    \int_a^c ydx=\int_{t_0}^{t_1} y(t) d(x(t))=\int_{t_0}^{t_1} b\sinh(t) a\sinh(t)dt.

    You can find the limits in terms of t right?
    i only submitted the x one....is that ok?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Aug 2008
    Posts
    903
    Yes, that's fine what you did. Sorry, I didn't notice that initially. And you know of course to express the limits of integration in t which I get:

    ab\int_0^{x_0} \sinh^2(t)dt
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Area under hyperbola
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 20th 2010, 11:47 AM
  2. Replies: 4
    Last Post: November 25th 2009, 06:47 AM
  3. area of the region bounded by the hyperbola?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 9th 2009, 03:07 PM
  4. area of a hyperbola
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 4th 2009, 11:50 PM
  5. Calculate an area
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 29th 2009, 05:16 AM

Search Tags


/mathhelpforum @mathhelpforum