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C4 integration Question

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    Hiya, I'm having abit of trouble integrating the following term between the limits of 0 and Pie/6.

    Y=Sec22X Tan22X
    Thanks for any help.
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    Differentiate tan3
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    (Original post by puttycat1)
    Hiya, I'm having abit of trouble integrating the following term between the limits of 0 and Pie/6.



    Thanks for any help.
    Understand the difference between 'pi' and 'pie'.

    For solving the question, try differentiating,  tan^32x
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    Can you do integration by parts?
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    (Original post by hcam)
    Can you do integration by parts?
    There is no need to do it.

    Just differentiate  tan^32x  and see what you get.
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    use the substitution u=tanx, then dx=1/sec^2x.du and this cancels so you're left with the integral of u^2, remember to change your limits though
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    sorry didn't realise it was 2x! I'm sure it won't make a huge difference though if you follow the same principle
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    You could do a substitution, let u=tan(2x)

    Edit- I was beaten to it. Remember chain rule when finding du/dx.
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    May I ask where the tan^3 2X comes from?
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    (Original post by shanban)
    use the substitution u=tanx, then dx=1/sec^2x.du and this cancels so you're left with the integral of u^2, remember to change your limits though

    (Original post by finality)
    You could do a substitution, let u=tan(2x)

    I find it interesting that people advocate substitution ... in order to spot this you would need to spot that sec2 is the derivative of tan ... then if you spot that why don't you just see that it is tan3 with a bit of numerical adjustment
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    (Original post by puttycat1)
    May I ask where the tan^3 2X comes from?
    the fact that sec2 is the derivative of tan

    and an understanding of the chain rule
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    (Original post by puttycat1)
    May I ask where the tan^3 2X comes from?
    It is just a technique of integration.

    Sometimes integrals are of the type,  \displaystyle \int f'(x)(f(x))^n \ dx , so to integrate them, first try to differentiate,  (f(x))^{n+1}
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    (Original post by TenOfThem)
    I find it interesting that people advocate substitution ... in order to spot this you would need to spot that sec2 is the derivative of tan ... then if you spot that why don't you just see that it is tan3 with a bit of numerical adjustment
    yeah I suppose, just easier to get the method marks with the other method?

    Also wouldn't it be (tan^3)/3?
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    (Original post by shanban)
    /3?

    Numerical adjustment

    Consider also the 2x
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    (Original post by TenOfThem)
    Numerical adjustment

    Consider also the 2x
    Oh yes of course, sorry!
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    (Original post by TenOfThem)
    I find it interesting that people advocate substitution ... in order to spot this you would need to spot that sec2 is the derivative of tan ... then if you spot that why don't you just see that it is tan3 with a bit of numerical adjustment
    But the integral here is (tan32x)/6
    or am I missing something?
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    (Original post by finality)
    But the integral here is (tan32x)/6
    or am I missing something?
    No ... that is what I said
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    (Original post by TenOfThem)
    No ... that is what I said
    Oh, is that what you meant by numerical adjustment? I thought you were saying it was just tan32x
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    (Original post by finality)
    Oh, is that what you meant by numerical adjustment? I thought you were saying it was just tan32x
    Aaaaah ... no

    My point was

    Spot that it is tan cubed and adjust as needed

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