Results 1 to 15 of 15

Math Help - Evaluate sig x(x+1)^1/2 .dx

  1. #1
    Junior Member
    Joined
    Oct 2013
    From
    Australia
    Posts
    45

    Evaluate sig x(x+1)^1/2 .dx

    Could someone give me a leg-up for this question?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Evaluate sig x(x+1)^1/2 .dx

    Hey Darrylcwc.

    What does sig mean? Is it the signum function? Something else?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2013
    From
    Australia
    Posts
    45

    Re: Evaluate sig x(x+1)^1/2 .dx

    Yes it refers to the sigma function
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Evaluate sig x(x+1)^1/2 .dx

    Is the range restricted to x >= -1? (In order to have only real solutions)?

    If so then you should consider the intervals [-1,0) and [0,whatever]. Also you will have to put a constraint on the limits if you want a finite answer.

    Recall that x(x+1)^(1/2) is an increasing function which should make your job easier.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Oct 2013
    From
    Australia
    Posts
    45

    Re: Evaluate sig x(x+1)^1/2 .dx

    Sorry I wasn't clear. I need to find the integral.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Evaluate sig x(x+1)^1/2 .dx

    Basically the signum function is -1 if x < 0, 0 if x = 0 and 1 if x > 0.

    You need to find when the function is < 0, 0, and > 0.

    x(x+1)^(1/2) = 0 implies x = 0 or x = -1.

    This means sig (x(x+1)^1/2) when x > 0 = 1 and this means Integral 0 to u sig(x(x+1)^(1/2)) = Integral 0 to u 1dx = u - 0 = u.

    Now you need to find when x(x+1)^(1/2) < 0 and for that region use sig(x(x+1)^(1/2)) = -1 when the condition is satisfied.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Sep 2013
    From
    USA
    Posts
    255
    Thanks
    114

    Re: Evaluate sig x(x+1)^1/2 .dx

    Quote Originally Posted by Darrylcwc View Post
    Sorry I wasn't clear. I need to find the integral.
    Try change of variable such as u = x + 1, and rewrite the sqrt as a power 1/2
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Oct 2013
    From
    Australia
    Posts
    45

    Re: Evaluate sig x(x+1)^1/2 .dx

    Quote Originally Posted by votan View Post
    Try change of variable such as u = x + 1, and rewrite the sqrt as a power 1/2
    Did so before you suggested. It was futile.

    The range is from 2 to -2: The integral I arrived at was: [u^2/2 - 10u].2u^(0.5); it's wrong.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Senior Member
    Joined
    Sep 2013
    From
    USA
    Posts
    255
    Thanks
    114

    Re: Evaluate sig x(x+1)^1/2 .dx

    Quote Originally Posted by Darrylcwc View Post
    Did so before you suggested. It was futile.

    The range is from 2 to -2: The integral I arrived at was: [u^2/2 - 10u].2u^(0.5); it's wrong.
    Evaluate sig x(x+1)^1/2 .dx-untitled2.gif

    are your limits of integration on u or on x. If they are for x convert them to u and you are set
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Evaluate sig x(x+1)^1/2 .dx

    Forget that way: just find when the expression inside the signum function is positive, negative, and 0 and replace it with +1, -1, and 0 respectively and integrate it piece-wise. (For example if u is positive for sig(u) then replace sig(u(x))dx with +1dx.)
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Junior Member
    Joined
    Oct 2013
    From
    Australia
    Posts
    45

    Re: Evaluate sig x(x+1)^1/2 .dx

    Quote Originally Posted by votan View Post
    Click image for larger version. 

Name:	untitled2.gif 
Views:	3 
Size:	7.1 KB 
ID:	29454

    are your limits of integration on u or on x. If they are for x convert them to u and you are set
    What about integrate x/[(3x+10)^0.5].dx from the range of 2 to -2
    I let u = 3x + 10 and x = [u-10]/3
    du/dx = 3
    dx = du/3
    I keep arriving at [2u^3/2]/3 - 20u^(0.5)

    Tried but again not working out
    Last edited by Darrylcwc; October 12th 2013 at 09:41 PM.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Senior Member
    Joined
    Sep 2013
    From
    USA
    Posts
    255
    Thanks
    114

    Re: Evaluate sig x(x+1)^1/2 .dx

    Quote Originally Posted by Darrylcwc View Post
    What about integrate x/[(3x+10)^0.5].dx from the range of 2 to -2
    I let u = 3x + 10 and x = [u-10]/3
    du/dx = 3
    dx = du/3
    I keep arriving at [2u^3/2]/3 - 20u^(0.5)

    Tried but again not working out
    Are you integrating y = x(3x+10)^(-0.5) or signum function sig[y]
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Junior Member
    Joined
    Oct 2013
    From
    Australia
    Posts
    45

    Re: Evaluate sig x(x+1)^1/2 .dx

    Quote Originally Posted by votan View Post
    Are you integrating y = x(3x+10)^(-0.5) or signum function sig[y]
    I'm trying to integrate the function x(3x+10)^(-0.5) and thereafter taking the function f(2) - f(-2)

    The antiderivative I arrived at is [2u^3/2]/3 - 20u^(0.5)

    When I tried f(2) - f(-2), i keep getting the wrong answer.
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Senior Member
    Joined
    Sep 2013
    From
    USA
    Posts
    255
    Thanks
    114

    Re: Evaluate sig x(x+1)^1/2 .dx

    Quote Originally Posted by Darrylcwc View Post
    I'm trying to integrate the function x(3x+10)^(-0.5) and thereafter taking the function f(2) - f(-2)

    The antiderivative I arrived at is [2u^3/2]/3 - 20u^(0.5)

    When I tried f(2) - f(-2), i keep getting the wrong answer.
    Evaluate sig x(x+1)^1/2 .dx-untitled2.gif
    Follow Math Help Forum on Facebook and Google+

  15. #15
    Junior Member
    Joined
    Oct 2013
    From
    Australia
    Posts
    45

    Re: Evaluate sig x(x+1)^1/2 .dx

    Quote Originally Posted by votan View Post
    Click image for larger version. 

Name:	untitled2.gif 
Views:	5 
Size:	8.3 KB 
ID:	29457
    Solved.
    Last edited by Darrylcwc; October 13th 2013 at 12:25 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Evaluate (A+1)(A-I)
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 19th 2011, 07:07 AM
  2. Evaluate 1-2(cos^2)25/1-2(sin^2)65
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 20th 2010, 09:15 AM
  3. how would I Evaluate this??
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 20th 2010, 07:51 PM
  4. evaluate
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 21st 2009, 03:26 AM
  5. Evaluate
    Posted in the Calculus Forum
    Replies: 7
    Last Post: November 17th 2009, 10:13 AM

Search Tags


/mathhelpforum @mathhelpforum