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    My brain isn't working properly today, and while revising c4 I managed to confuse myself.

    Why can't you integrate for example sin^2 (x) using inverse chain rule, ie increase power by 1, divide by new power, divide by differential of sinx to get (tanx sin^2 x)/3 ?
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    What's the inverse chain rule?
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    Well actually ye it's not in the OCR book but it's how my teacher describes it. Like if you were differentiating (2x)^2 you could multiply by power, reduce power by 1, multiply by differential of whats in the brackets getting 2x2x(2x) = 8x

    So doing it the other way around basically, like if I was integrating (2x)^2 I could increase the power by 1, divide by the new power, divide by differential of whats in the brackets ie (2x)^3 / (3 x 2) = 4x^3 / 3 +k or w/e but ye.
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    (Original post by SimonM)
    What's the inverse chain rule?
    I think that's what they call integration by substitution :confused:
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    (Original post by jamie092)
    My brain isn't working properly today, and while revising c4 I managed to confuse myself.

    Why can't you integrate for example sin^2 (x) using inverse chain rule, ie increase power by 1, divide by new power, divide by differential of sinx to get (tanx sin^2 x)/3 ?
    You can't start dividing by functions of x, you can only adjust numerical factors. You can also check if you're wrong. Try differentiating what you think you'd get. You don't get back to what you want.
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    Call it reverse chain, not inverse
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    (Original post by boromir9111)
    I think that's what they call integration by substitution :confused:
    I think he might mean by "by inspection." But don't hold me to it.
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    (Original post by dknt)
    I think he might mean by "by inspection." But don't hold me to it.
    Ahh yes, there was a thread on this a while ago, didn't end well lol but inspection is a form of substitution.....loonggg!
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    (Original post by dknt)
    You can't start dividing by functions of x, you can only adjust numerical factors. You can also check if you're wrong. Try differentiating what you think you'd get. You don't get back to what you want.
    Hmm so you can't divide by functions of x when you integrate but you can multiply by functions of x when you differentiate? weird; P
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    (Original post by jamie092)
    Hmm so you can't divide by functions of x when you integrate but you can multiply by functions of x when you differentiate? weird; P
    What?

    What I mean is you can only adjust numerical factors. When you integrate, sometimes you can do it by inspection and use a little bit of prior knowledge to "guess" the derivative. You then check by differentiating and then adjust the numerical factor. For example, if you differentiate and end up with a 2 in front, but you need a 3, you adjust the numerical factor to (3/2) to give you this. But if you end up with an extra "x" term, which you don't have in your integral, you can't put a (1/x) in front of it.
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    (Original post by dknt)
    What?

    What I mean is you can only adjust numerical factors. When you integrate, sometimes you can do it by inspection and use a little bit of prior knowledge to "guess" the derivative. You then check by differentiating and then adjust the numerical factor. For example, if you differentiate and end up with a 2 in front, but you need a 3, you adjust the numerical factor to (3/2) to give you this. But if you end up with an extra "x" term, which you don't have in your integral, you can't put a (1/x) in front of it.
    Well ye I know that I suppose it's just something I'm going to have to ask my teacher since I can't really explain what I mean here ;P.
 
 
 
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