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Homework Help: Help in integration

  1. Jun 9, 2008 #1
    can someone integrate that problem

    x^2 cos (x^5) dx

    i tried integration by parts but i didn't get anything
     
  2. jcsd
  3. Jun 9, 2008 #2
    There might be something wrong with the question if you are in an introductory course

    some mess:

    f =

    x^2*cos(x^5)


    >> int(f,x)

    ans =

    1/10*2^(3/5)*pi^(1/2)*(5/3/pi^(1/2)/x^2*2^(2/5)
    *sin(x^5)+5/3/pi^(1/2)/x^2*2^(2/5)*(cos(x^5)
    *x^5-sin(x^5))-2/3/pi^(1/2)*x^8*2^(2/5)/(x^5)^(11/10)
    *sin(x^5)*LommelS1(1/10,3/2,x^5)-5/3/pi^(1/2)*x^8
    *2^(2/5)/(x^5)^(21/10)*(cos(x^5)*x^5-sin(x^5))
    *LommelS1(11/10,1/2,x^5))


    >> f = x^2*(cos(x))^5

    f =

    x^2*cos(x)^5


    >> int(f,x)

    ans =

    x^2*(1/5*cos(x)^4*sin(x)+4/15*cos(x)^2*
    sin(x)+8/15*sin(x))+2/25*x*cos(x)^5-2/125*
    cos(x)^4*sin(x)-272/3375*cos(x)^2*sin(x)-4144/3375*
    sin(x)+8/45*x*cos(x)^3+16/15*x*cos(x)
     
  4. Jun 9, 2008 #3
    no there is nothing wrong with the problem and iam in what called in our country differentiation and integration 2 like calculus 3
    and the original problem is from my exam {{ and i didn't solve it but i'm curious }}



    given____ { int from 0 to 4 }{int from y^1/2 to 2 } cos(x^5) dx dy ____ reverse the order of integration and evaluate the resulting intgerals .


    after reversing , it will be ______ x^2 cos (x^5) dx _______ and the inequalities dosent matter
     
  5. Jun 9, 2008 #4

    Vid

    User Avatar

    You reversed the order of integration. You intergrate with wrt y first, dydx.
     
    Last edited: Jun 9, 2008
  6. Jun 10, 2008 #5
    so what is the solution of the integration pls
     
  7. Jun 10, 2008 #6

    Kurdt

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Are you sure it was [itex] \cos(x^5)[/itex]? You really couldn't integrate that on a test. The method for reversing the order of integration is fairly simple. You first need to sketch the area of integration on a graph and then find the limits for integrating over y with x constant and then the limits for integrating over x with y constant.
     
  8. Jun 11, 2008 #7
    i'm absolutely sure that it's int of x^2 cos(x^5) dx

    dose anyone have any idea ????????????
     
  9. Jun 11, 2008 #8
    What was the original question? We've already proved that the integral you post is too difficult!
     
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