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Math Help - Integral problem :(

  1. #1
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    Integral problem :(

    Could someone solve this for me please?
    I haven't got an idea how to solve this, therefore
    please provide answer and show step-by-step would be really appreciated..
    Thank you.

    a) 2e^(7x)/e^(5x) dx

    b)x^2 sqrt (7-3x^3) dx

    c) x^3 sqrt ( x-3) dx

    Thank you! I don't need an explanation, I'll try to find out by my self,
    therefore please get me easy working + answer
    Thanks
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by kunkka View Post
    Could someone solve this for me please?
    I haven't got an idea how to solve this, therefore
    please provide answer and show step-by-step would be really appreciated..
    Thank you.

    a) 2e^(7x)/e^(5x) dx

    b)x^2 sqrt (7-3x^3) dx

    c) x^3 sqrt ( x-3) dx

    Thank you! I don't need an explanation, I'll try to find out by my self,
    therefore please get me easy working + answer
    Thanks
    It's against the forum rules to completely give you the answer and working unless you've shown your working

    a) 2\dfrac{e^{7x}}{e^{5x}} = 2e^{7x-5x} = 2e^{2x}

    Use the rule: \int e^{ax} = \dfrac{1}{a}e^{ax}

    b) This requires you to use integration by parts twice

    Integration by parts: \int u\,dv = uv - \int v\,du

    Let u = x^2 to get you started.

    c) As above but use it three times


    If you do not understand show how far you get
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  3. #3
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    Just in case a picture helps for b)...



    ... where (key in spoiler) ...

    Spoiler:


    ... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case x), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

    The general drift is...



    Similarly, for c), using u = sqrt(x-3), i.e. x = u^2 + 3...



    Fill the blanks and continue the anti-clockwise journey towards the integral, I.

    _________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Last edited by tom@ballooncalculus; October 18th 2010 at 02:10 PM.
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  4. #4
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    Thanks alot for your help!!!!!!
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  5. #5
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    Quote Originally Posted by kunkka View Post
    [snip]

    b)x^2 sqrt (7-3x^3) dx

    c) x^3 sqrt ( x-3) dx

    Thank you! I don't need an explanation, I'll try to find out by my self,
    therefore please get me easy working + answer
    Thanks
    b) Substitute u = 7 - 3x^3.

    c) Substitute u = x - 3. Then expand (u+3)^3 u^{1/2} and integrate term-by-term.
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