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Edexcel A2 C4 Mathematics June 2016 - Official Thread Watch

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    (Original post by BBeyond)
    ...
    You and other might enjoy this, I'll give a bit of guidance to ease things out.

    6. Prove that \displaystyle \int_0^{\pi} xf(\sin x) \, \mathrm{d}x = \frac{\pi}{2}\int_0^{\pi} f(\sin x) \, \mathrm{d}x

    7. Evaluate \displaystyle \int_0^{\pi} x\ln(\sin x) \, \mathrm{d}x
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    (Original post by BBeyond)
    Is there a quicker way of doing that? Buzzing with that though ahah didn't even know about this trick until today. I think that might be a bit past my level lol
    Slightly, but not by very much. I'll post it up later if you want. :yep:

    The general trick is if we have a well enough behaved f, then:

    \displaystyle 

\begin{equation*}\int_a^b f(x) \, \mathrm{d}x = \int_a^b f(a + b - x) \, \mathrm{d}x \end{equation*}

    by using the substitution x \mapsto a + b - x. :-)
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    (Original post by Zacken)
    Slightly, but not by very much. I'll post it up later if you want. :yep:

    The general trick is if we have a well enough behaved f, then:

    \displaystyle 

\begin{equation*}\int_a^b f(x) \, \mathrm{d}x = \int_a^b f(a + b - x) \, \mathrm{d}x \end{equation*}

    by using the substitution x \mapsto a + b - x. :-)
    So is that a rule we could quote at a-level? (Not that I'd ever need to tbf ahah)

    (Original post by Zacken)
    You and other might enjoy this, I'll give a bit of guidance to ease things out.

    6. Prove that \displaystyle \int_0^{\pi} xf(\sin x) \, \mathrm{d}x = \frac{\pi}{2}\int_0^{\pi} f(\sin x) \, \mathrm{d}x

    7. Evaluate \displaystyle \int_0^{\pi} x\ln(\sin x) \, \mathrm{d}x
    I'm tutoring in 15 mins but I'll have a look later, cheers!
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    (Original post by BBeyond)
    So is that a rule we could quote at a-level? (Not that I'd ever need to tbf ahah)
    Well, not quite sure why you'd need to quote it. It's literally write down u = a + b - x and you're done in one line.

    I'm tutoring in 15 mins but I'll have a look later, cheers!
    Awesome, have fun. :yep:
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    (Original post by Zacken)
    6. Prove that \displaystyle \int_0^{\pi} xf(\sin x) \, \mathrm{d}x = \frac{\pi}{2}\int_0^{\pi} f(\sin x) \, \mathrm{d}x
    I think that's enough Maths for me for today...
    Spoiler:
    Show
    I = \displaystyle \int_{0}^{\pi} xf(\mathrm{sin}x) \mathrm{d}x

    y=\pi - x

    \dfrac{dy}{dx} = -1\ \ \therefore - dy = dx

    =\displaystyle -\int_{0}^{\pi} (\pi - y)f(\mathrm{sin}(\pi - y)) \mathrm{d}y

    Going back to:

    y=\pi - x

    - dy = dx

    And expanding (\pi - x)f(sinx)


    =\displaystyle \pi\int_{0}^{\pi} f(\mathrm{sin}x) \mathrm{d}x - \displaystyle \int_{0}^{\pi} x f(\mathrm{sin}x) \mathrm{d}x

    \therefore I = \displaystyle \pi\int_{0}^{\pi} f(\mathrm{sin}x) \mathrm{d}x - I

    2I = \displaystyle \pi\int_{0}^{\pi} f(\mathrm{sin}x) \mathrm{d}x

    I = \displaystyle \dfrac{\pi}{2}\int_{0}^{\pi} f(\mathrm{sin}x) \mathrm{d}x
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    (Original post by edothero)
    I think that's enough Maths for me for today...
    :borat: Awesome work.
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    (Original post by Zacken)
    You and other might enjoy this, I'll give a bit of guidance to ease things out.

    6. Prove that \displaystyle \int_0^{\pi} xf(\sin x) \, \mathrm{d}x = \frac{\pi}{2}\int_0^{\pi} f(\sin x) \, \mathrm{d}x

    7. Evaluate \displaystyle \int_0^{\pi} x\ln(\sin x) \, \mathrm{d}x
    6 better not be a C4 past question. Jheez

    7 looks easy though
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    (Original post by Lawliettt)
    6 better not be a C4 past question. Jheez

    7 looks easy though
    6 is far easier than 7. But no, none of these are past exam questions. Just really extension-y ones.
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    I don't like vectors :getmecoat:
    Too repetitive
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    (Original post by Serine Soul)
    I don't like vectors :getmecoat:
    Too repetitive
    Nobody likes vectors...
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    (Original post by Serine Soul)
    I don't like vectors :getmecoat:
    Too repetitive
    They're actually pretty fun if you look at them outside the treatment that A-Level gives them!
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    (Original post by Zacken)
    6 is far easier than 7. But no, none of these are past exam questions. Just really extension-y ones.
    7 just looks like it can be done using intergration by parts. There wouldn't be much thinking involved in that case. That being said, I haven't attempted them yet. I'll try later.

    On another note, I literally haven't started vectors at all. And I know they're also in M1. How long will it take for me to learn C4 and M1 vectors from scratch?
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    (Original post by Lawliettt)
    7 just looks like it can be done using intergration by parts. There wouldn't be much thinking involved in that case. That being said, I haven't attempted them yet. I'll try later.
    You'd be best served using the result from question 6 to do question 7. There'd quite a bit of thinking involved, methinks. Have a go.

    On another note, I literally haven't started vectors at all. And I know they're also in M1. How long will it take for me to learn C4 and M1 vectors from scratch?
    A few hours.
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    (Original post by 13 1 20 8 42)
    Nobody likes vectors...
    Glad to know I'm not alone


    (Original post by Zacken)
    They're actually pretty fun if you look at them outside the treatment that A-Level gives them!
    Nah, cba doing that :rofl:
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    Struggling for maths motivation


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    • Very Important Poster
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    (Original post by thad33)
    Struggling for maths motivation


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    :five:
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    (Original post by thad33)
    Struggling for maths motivation


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    :hugs:
    Just remember that you need to meet an offer for a uni (if uni's your plan) and that should motivate you :yep:
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    (Original post by Serine Soul)
    :hugs:
    Just remember that you need to meet an offer for a uni (if uni's your plan) and that should motivate you :yep:
    You'd think it would. I might do a few days of Chem instead.

    I'll be majorly ****ed off if I don't get an A* after this.


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    (Original post by thad33)
    You'd think it would. I might do a few days of Chem instead.

    I'll be majorly ****ed off if I don't get an A* after this.


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    That's honestly how I feel every time I see a question on vectors

    But remember that you need to distribute your work accordingly to all your subjects to maximise your grades in all three

    That said, I do more work for maths (so much homework ) than an other subject, and I'm least fussed about not getting A* in Maths aha
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    (Original post by Serine Soul)
    That's honestly how I feel every time I see a question on vectors

    But remember that you need to distribute your work accordingly to all your subjects to maximise your grades in all three

    That said, I do more work for maths (so much homework ) than an other subject, and I'm least fussed about not getting A* in Maths aha
    I've done far too much on trig the past few days. I can't wait until past papers so it isn't so monotonous.

    Vectors are **** as well. I think I only really like calculus.

    I just seem to work better when I revise in chunks of certain subjects. I'll try and do half Chem half maths for the next week so I don't get too bored.

    Right, back to the grind...


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