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Thread: Problem with definate integrals?

  1. #1
    New Member
    Join Date
    Apr 2012
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    18

    Problem with definate integrals?

    First make a substitution and then use integration by parts to evaluate the integral:

    [tex]\int[/tex] sin (sqrt x)dx

    This is what I have done up to now:

    dv = dx
    v = x
    sin (sqrt x) = u
    (0.5 cos (sqrt x))/ sqrt (x) = du

    x sin (sqrt x) - [tex]\int[/tex] (0.5x cos (sqrt x))/ sqrt (x)dx

  2. #2
    Elite Member
    Join Date
    Jun 2007
    Posts
    12,298
    Quote Originally Posted by twohaha View Post
    First make a substitution and then use integration by parts to evaluate the integral:

    [tex]\int[/tex] sin (sqrt x)dx

    This is what I have done up to now:

    dv = dx
    v = x
    sin (sqrt x) = u
    (0.5 cos (sqrt x))/ sqrt (x) = du

    x sin (sqrt x) - [tex]\int[/tex] (0.5x cos (sqrt x))/ sqrt (x)dx
    [tex]\int[/tex] sin (sqrt x)dx

    substitute

    u = √x → u2 = x → dx = 2u du

    [tex]\int[/tex] sin (sqrt x)dx = 2[tex]\int[/tex] u * sin (u)du

    Now use integration by parts.......
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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