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Edexcel A2 C4 Mathematics June 2016 - Official Thread

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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 ∫0πxf(sin⁡x) dx=π2∫0πf(sin⁡x) dx\displaystyle \int_0^{\pi} xf(\sin x) \, \mathrm{d}x = \frac{\pi}{2}\int_0^{\pi} f(\sin x) \, \mathrm{d}x

7. Evaluate ∫0πxln⁡(sin⁡x) dx\displaystyle \int_0^{\pi} x\ln(\sin x) \, \mathrm{d}x
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 ff, then:

Unparseable latex formula:

\displaystyle [br]\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↦a+b−xx \mapsto a + b - x. :-)
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 ff, then:

Unparseable latex formula:

\displaystyle [br]\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↦a+b−xx \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 ∫0πxf(sin⁡x) dx=π2∫0πf(sin⁡x) dx\displaystyle \int_0^{\pi} xf(\sin x) \, \mathrm{d}x = \frac{\pi}{2}\int_0^{\pi} f(\sin x) \, \mathrm{d}x

7. Evaluate ∫0πxln⁡(sin⁡x) dx\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!
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−xu = 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:
Original post by Zacken

6. Prove that ∫0πxf(sin⁡x) dx=π2∫0πf(sin⁡x) dx\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

Original post by edothero
I think that's enough Maths for me for today...


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

6. Prove that ∫0πxf(sin⁡x) dx=π2∫0πf(sin⁡x) dx\displaystyle \int_0^{\pi} xf(\sin x) \, \mathrm{d}x = \frac{\pi}{2}\int_0^{\pi} f(\sin x) \, \mathrm{d}x

7. Evaluate ∫0πxln⁡(sin⁡x) dx\displaystyle \int_0^{\pi} x\ln(\sin x) \, \mathrm{d}x


6 better not be a C4 past question. Jheez :frown:

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

7 looks easy though


6 is far easier than 7. But no, none of these are past exam questions. Just really extension-y ones.
I don't like vectors :getmecoat:
Too repetitive
Original post by Serine Soul
I don't like vectors :getmecoat:
Too repetitive


Nobody likes vectors...
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!
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?
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.
Original post by 1 8 13 20 42
Nobody likes vectors...

Glad to know I'm not alone :colonhash:


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:
Struggling for maths motivation


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Original post by thad33
Struggling for maths motivation


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:five:
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:
(edited 8 years ago)
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 :angry:

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

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

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

That said, I do more work for maths (so much homework :colonhash:) 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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