Results 1 to 1 of 1

Thread: How to simplify an integral?

  1. #1
    Nov 2010

    How to simplify an integral?

    My problem is to simplify the following integral:
    <br />
G=\int_{x=0}^{1}{exp{(tx+kx^{1.5})}}\,dx<br />
    I have a solution, but can't understand it without explanations. The solution is following:
    1) k>{\frac{2}{3}t}
    G_1={\frac{4}{3}}{\frac{\sqrt{\pi}}{k}{t^{1.5}}}ex  p({{\frac{4}{27}}{t^3}k^{-2})
    2) k<{\frac{2}{3}t}
    G_2={\frac{1}{2}}{{\sqrt{\frac{\pi}{a}}}exp{\left(  {\frac{b^2-ac}{c}}\right)erfc\left({\frac{b}{\sqrt{a}}}\right  ), where a={\frac{3}{8}}t, b={\frac{1}{2}}t-{\frac{3}{4}}k, c=k-t
    The second case is clear: we expand the exponential term to the 2nd order Taylor series around u=1, simplify the expression, change variable, set the lower integration linit from 0 to -\infty and get the complimentary error function. But the first case result is not clear at all. Please, help me to understand. Thank you.
    Last edited by nik4214; Nov 16th 2010 at 09:56 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Simplify the integral (is my version correct?)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Apr 6th 2011, 09:45 AM
  2. How to simplify this (line) integral?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Mar 30th 2011, 10:33 AM
  3. Replies: 2
    Last Post: Feb 27th 2010, 11:22 PM
  4. Need to simplify multiple integral
    Posted in the Statistics Forum
    Replies: 0
    Last Post: Mar 29th 2008, 01:58 PM
  5. Simplify
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Mar 8th 2007, 08:35 AM

Search Tags

/mathhelpforum @mathhelpforum