Results 1 to 6 of 6

Math Help - Integral - infinite limit

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    27

    Integral - infinite limit

    \displaystyle\int^\infty_1 \frac{1}{x^5}\,dx

    How is this calculated?

    What is the name of these types of integrals (with infinite in limits and fractions in integrand)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    May 2009
    Posts
    471
    Quote Originally Posted by anon_404 View Post
    \displaystyle\int^\infty_1 \frac{1}{x^5}\,dx

    How is this calculated?

    What is the name of these types of integrals (with infinite in limits and fractions in integrand)?

    This is known as an improper integral because the upper bound is infinity

    \int_a^\infty f(x)dx=\lim_{b\rightarrow\infty}\int_a^b f(x)dx

    =\lim_{b\rightarrow\infty}F(b)-F(a)

    where F'(x)=f(x)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2009
    Posts
    27
    How is it calculated?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    May 2009
    Posts
    471
    My previous post tells you to evaluate the antiderivative, plug in a variable for the uppper limit and then subtract the antiderivative evaluated at the lower limit, and take the limit as your variable goes to infinity

    \displaystyle\int \frac{1}{x^5}dx=-\frac{1}{4x^4}+c


    You should be able to solve your question now
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by anon_404 View Post
    How is it calculated?
    The first step is to write \lim_{\alpha \rightarrow + \infty} \int_1^{\alpha} \frac{1}{x^5} \, dx.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466
    Perhaps it would help you to write \frac{1}{x^5} as x^{-5}. Do you know the anti-derivative of x^n?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. infinite Limit
    Posted in the Calculus Forum
    Replies: 6
    Last Post: August 23rd 2010, 05:53 PM
  2. Infinite Sum Limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 24th 2010, 04:53 PM
  3. infinite limit
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: August 29th 2009, 08:10 PM
  4. Infinite Limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 24th 2008, 06:33 PM
  5. need help plz infinite limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 8th 2006, 07:06 AM

Search Tags


/mathhelpforum @mathhelpforum