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Math Help - integration

  1. #1
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    integration

    hii!

    how do you evaluate this integral.

    thanks guys
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  2. #2
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    Let w = sqr(x)

    x = w^2

    dx = 2wdw

    then your thing becomes.

    integral [ (1/w) * 2w * sinw dw ]

    the 2 w's cancel so your left with

    integral [ 2 sin(w) dw ]

    I think you can get the rest from there
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  3. #3
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    (this one should be incorrect, ill check my notes later)


    OR possibly



    I think 2nd one is correct.
    Last edited by r_maths; May 1st 2007 at 03:20 PM.
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  4. #4
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    OR possibly



    I think 2nd one is correct.

    R_math... try using the substitute method.
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  5. #5
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    I dunno why but I prefer the way I did it, provided I get it right of course.
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  6. #6
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by r_maths View Post
    I dunno why but I prefer the way I did it, provided I get it right of course.

    I'm sorry to say but that wasn't right.

    sine and cosine are functions, not constants. When you have sin(theta) that is not the same as sine * theta. If you have sin(theta)/theta, you cannot "reduce" the theta's and declare that sin(theta)/theta = sin

    That doesn't make any sense.

    In the future, I would recommend you do it the way smooth did, using substitution.
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  7. #7
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    Quote Originally Posted by smoothi963 View Post
    Let w = sqr(x)

    x = w^2

    dx = 2wdw

    then your thing becomes.

    integral [ (1/w) * 2w * sinw dw ]

    the 2 w's cancel so your left with

    integral [ 2 sin(w) dw ]

    I think you can get the rest from there
    Thank you I like that method.

    = -2cosw ???
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  8. #8
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    Thank you I like that method.

    = -2cosw ???

    -2cosw + c.....but remember you substituted the w, so you will need to rewrite wat w was.

    -2cos(sqr(x)) + c
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  9. #9
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    Quote Originally Posted by ecMathGeek View Post
    I'm sorry to say but that wasn't right.

    sine and cosine are functions, not constants. When you have sin(theta) that is not the same as sine * theta. If you have sin(theta)/theta, you cannot "reduce" the theta's and declare that sin(theta)/theta = sin

    That doesn't make any sense.

    In the future, I would recommend you do it the way smooth did, using substitution.
    Thanks, i'll remember that next time.

    ----

    Enita, no need to thank me. I gave you wrong solution.
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