Results 1 to 3 of 3

Thread: Integral with parameter and Beta/Gamma Function

  1. #1
    Member
    Joined
    May 2012
    From
    slovenia
    Posts
    90
    Thanks
    5

    Exclamation Integral with parameter and Beta/Gamma Function

    Hello, guys ...

    1. Calculate the integral $\displaystyle \int_{0}^{1}\left(\dfrac{x}{1 + \sqrt{1-x}}\right)^{\frac{3}{2}}dx$ with the help of $\displaystyle \Gamma$ and $\displaystyle B$.

    2. We are given integral with a parameter $\displaystyle F(t) = \int_{1}^{2}\arctan\frac{t}{x}dx$. Find its derivative $\displaystyle F'(t)$.

    Please help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2013
    From
    Lebanon
    Posts
    907
    Thanks
    434

    Re: Integral with parameter and Beta/Gamma Function

    2.

    $\displaystyle F'(t)=\int_1^2 \frac{\partial }{\partial t}\left(\arctan \left(\frac{t}{x}\right)\right) \, dx=\int_1^2 \frac{x}{t^2+x^2} \, dx$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2012
    From
    slovenia
    Posts
    90
    Thanks
    5

    Re: Integral with parameter and Beta/Gamma Function

    $\displaystyle \int_{1}^{2}\dfrac{x}{t^2 + x^2}dx = \int_{t^2 + 1}^{t^2 + 4}\dfrac{du}{2u} = \dfrac{1}{2}\ln\left|u\right| \big|_{t^2+1}^{t^2 + 4} = \dfrac{1}{2}\ln(\dfrac{t^2+4}{t^2+1})$ Right?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. got stuck with beta gamma function need help
    Posted in the New Users Forum
    Replies: 1
    Last Post: Mar 13th 2013, 02:08 PM
  2. Gamma Beta Function
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Aug 22nd 2011, 05:46 AM
  3. Gamma - Gamma parameter estimation EM algorithm
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: Jul 24th 2010, 10:53 AM
  4. Replies: 1
    Last Post: Jan 6th 2010, 11:13 PM
  5. [SOLVED] using beta or gamma function
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Jan 6th 2010, 12:02 AM

/mathhelpforum @mathhelpforum