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    (Original post by paraphilos)
    if y(x) = a^x, then \log(y) = x\log(a); thus by implicit differentiation: \dfrac{1}{y}\dfrac{dy}{dx} = \log(a) \implies \dfrac{dy}{dx} = y\log(a) \implies \boxed{\dfrac{dy}{dx} = a^x\log(a)}
    thank you!!!!!!!!!!!!!! :d
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    (Original post by physicsmaths)
    Use Chebysev's


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    Could you explain 4b and how you'd get that x=0.1?
    https://a086a5a2f39bda93734c56a63fab...%20Edexcel.pdf
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    Use U=cosx, and you should be good

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    (Original post by arsenalfc97)
    When finding the shortest distance from the point to a line, how can you assume that a right angle is made between the point and the line?
    Draw a line and draw a point. Draw random connections from that point to the line. You will bee the shortest distance is when the connection is perpendicular to the line
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    Hey can someone please explain to me June 2014, 7b and how the volume of a cone thing works- don't get it
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    (Original post by manlikem)
    what do you mean? The question is just integrate sinx cos^3 x dx
    The identity cos^2x + sin^2x = 1 is used when integrating odd powers of sinx and cosx.
    Integral of cos^3x
    = integral of cosx cos^2x
    = integral of cosx (1 - sin^2x)
    = integral of cosx - cosx sin^2x
    Then use integration of even powers of sinx
    Hope it helps
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    https://5a302d29ff432793ce79475dd3db...%20Edexcel.pdf

    how do you do Question 4?
    nvm
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    You cant do it by parts, as i keep going in loops and circles haha. I think you do it by inspection? which is something i cant do, but will have another try
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    Do we have to use the identical to sign when writing partial fractions or can we just use the '=' sign? Would we lose marks
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    If you ever have any integral involving both sine and cosine functions in C4, you can hazard a guess that some kind of substitution will be involved, seeing as one derives the other (more or less).
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    Can anyone explain question 8F from the IAL January 2014 paper (link: http://www.physicsandmathstutor.com/...rs/c4-edexcel/ )
    Thank you ^.^
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    (Original post by sj97)
    Could you explain 4b and how you'd get that x=0.1?
    https://a086a5a2f39bda93734c56a63fab...%20Edexcel.pdf

    (Original post by SeanFM)
    Well, you've expanded 8-9x cube rooted, and you're asked to find the cube root of 7100. So you ask yourself how you can make 8-9x look anything like 7100. Well, x=1/10 makes it 7.1, so using the expansion you get the cube root of 7.1. But we want the cube root of something a thousand times bigger.

    Just like (2*4)^2 = 8^2 = 64 = 4*16 = 2^2 * 4^2, the cube root of 7100 can be split into the cube root of 7.1 and the cube root of 1000 multiplied together. So you get the expansion for 7.1 and multiply by the cube root of 1000, which is 10.
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    First, separate the functions of the variables y and x and in doing so integrate both sides; remember:

    \dfrac{dy}{dx} = f(x)g(y) \implies \displaystyle\int \dfrac{1}{g(y)} dy = \displaystyle\int f(x) dx
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    (Original post by mb_12)
    The identity cos^2x + sin^2x = 1 is used when integrating odd powers of sinx and cosx.
    Integral of cos^3x
    = integral of cosx cos^2x
    = integral of cosx (1 - sin^2x)
    = integral of cosx - cosx sin^2x
    Then use integration of even powers of sinx
    Hope it helps
    So what what would you do exactly after you get cosx - cosx sin^2x ??
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    EDIT: Ignore, lol.
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    (Original post by mb_12)
    The identity cos^2x + sin^2x = 1 is used when integrating odd powers of sinx and cosx.
    Integral of cos^3x
    = integral of cosx cos^2x
    = integral of cosx (1 - sin^2x)
    = integral of cosx - cosx sin^2x
    Then use integration of even powers of sinx
    Hope it helps
    I think even then that is perhaps a little complicated; consider instead:

    \displaystyle\int \cos^3(x) dx = \displaystyle\int \cos(x)(1 - \sin^2(x)) dx, then, substitute u(x) := \sin(x).

    Although I am aware that the original question was to integrate a function of both sine and cosine, the above hopefully illustrates how to integrate an odd power of cosine (/sine).
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    (Original post by Paraphilos)
    First, separate the functions of the variables y and x and in doing so integrate both sides; remember:

    \dfrac{dy}{dx} = f(x)g(y) \implies \displaystyle\int \dfrac{1}{g(y)} dy = \displaystyle\int f(x) dx
    is it y=2(e^tan3x+1)?
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    (Original post by mb_12)
    The identity cos^2x + sin^2x = 1 is used when integrating odd powers of sinx and cosx.
    Integral of cos^3x
    = integral of cosx cos^2x
    = integral of cosx (1 - sin^2x)
    = integral of cosx - cosx sin^2x
    Then use integration of even powers of sinx
    Hope it helps
    thanks! and if I use substitution could I make cos x = u?
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    (Original post by Alice Moody)
    You cant do it by parts, as i keep going in loops and circles haha. I think you do it by inspection? which is something i cant do, but will have another try
    thanks for trying!
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    Hopefully vectors aint the last question, when it is its usually a mad ting


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