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Math Help - Need help with 2 questions

  1. #1
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    Need help with 2 questions

    1. Calculate the integrals of:

    a*x*sin(bx) dx
    and
    (x^2)(sin^2(ax)) dx
    where a and b are constants. hint: use double angle formula

    2. consider the improper integral

    integral from (2*sqrt(3)) to infiniti of: (24x^3)/(4+x^2)^(5/2) dx.
    EDIT: Make an appropriate trigonometric substitution to convert into a proper integral. Hence determine its value.

    Someone can help me with these please?
    Last edited by shadow85; August 28th 2008 at 04:11 AM.
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  2. #2
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    Quote Originally Posted by shadow85 View Post
    1. Calculate the integrals of:

    a*x*sin(bx) dx

    Mr F says: Use integration by parts.

    and
    (x^2)(sin^2(ax)) dx
    where a and b are constants. hint: use double angle formula
    Mr F says: {\color{red}\sin^2 (ax) = \frac{1}{2} \left( 1 - \cos (2ax) \right)}.

    Hint 2: Use integration by parts (twice).

    2. consider the improper integral

    integral from (2*sqrt(3)) to infiniti of: (24x^3)/(4+x^2)^(5/2) dx.
    EDIT: Make an appropriate trigonometric substitution to convert into a proper integral. Hence determine its value.

    Mr F says: Substitute {\color{red} x = 2 \tan t}.

    Someone can help me with these please?
    Since you've been set these questions I'm assuming you've been taught integration by parts and that you know how to make a substitution.

    If you need more help please show the working you've done and state exactly where you're stuck.


    By the way - bumping and begging for help is against the forum rules that you agreed to when you became a member.
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  3. #3
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    Sorry about the nagging, im just getting desperate, lol. Anyways thanks, I will work on what you said and see where I get from there.
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