Results 1 to 6 of 6

Math Help - Finding the Surface Area of the curve?

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    92

    Finding the Surface Area of the curve?

    Finding the Surface Area of the curve?

    y = 1/x
    1 ≤ x ≤ ∞ about x-axis.

    Thanks
    Last edited by racewithferrari; July 26th 2010 at 12:55 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    676
    Thanks
    19
    I didn't check through your integration, but when you have an improper integral \int_a^{\infty}f(x)dx, just compute the limit \lim_{b->\infty}\int_a^bf(x)dx

    Are you familiar with improper integrals?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2009
    Posts
    92
    After solving it, the answer come to ∞. Right?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    676
    Thanks
    19
    Quote Originally Posted by racewithferrari View Post
    After solving it, the answer come to ∞. Right?

    Actually, I think you have an error in your integration. I checked it, and there's a problem:

    \int \frac{1}{x}\sqrt{1+\frac{1}{x^4}dx

    Add the fractions in the radical \sqrt{\frac{x^4+1}{x^4}}=\frac{\sqrt{1+x^4}}{x^2}

    Plug this into the integral to get \int \frac{\sqrt{1+x^4}}{x^3}dx.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,108
    Thanks
    970
    \displaystyle \int_1^{\infty} \frac{\sqrt{1+x^4}}{x^3} \, dx > \int_1^{\infty} \frac{1}{x} \, dx

    note that it is rather easy to show that \displaystyle \int_1^{\infty} \frac{1}{x} \, dx diverges.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Nov 2009
    Posts
    92
    I did nothing wrong. I combined num and dem. The sqrt sign is on the top only.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. area of surface by rotating the curve
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 3rd 2010, 06:36 PM
  2. Replies: 11
    Last Post: April 29th 2010, 11:51 AM
  3. Replies: 2
    Last Post: April 19th 2010, 03:54 PM
  4. Surface Area Of A Parametric Curve?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 26th 2010, 01:37 PM
  5. Surface Area obtained by rotating the curve
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 3rd 2010, 03:12 PM

Search Tags


/mathhelpforum @mathhelpforum