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C4 (Not MEI) - Thursday June 21 2012, PM

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Original post by Killjoy-
They used integration by parts straight away and let u=lnx as when differentiated it is 1/x and that works out quite nicely.
I think that's a standard method which may come up often.

I tried substitution, it isn't the method they use but it works.
I let x=eyx=e^{-y} (You will see why I used y soon) and ended up with 0ln13yey dy\displaystyle\int^{ln\frac{1}{3}}_0 ye^y\ dy.

Then I applied integration by parts. If I used u earlier then it would get very confusing at this stage with u's and v's :P

Their alternative method involved substitution, but they ended up with the definite integral 0ln3tet dt\displaystyle\int^{ln3}_0 te^{-t}\ dt instead.
(And then they used integration by parts.)

Cool thanks, that was 10 part 2
But still thanks anyways..
Raheem94 helped me out already .. thanks :smile:
Reply 81
Original post by Smiley Face :)
Cool thanks, that was 10 part 2
But still thanks anyways..
Raheem94 helped me out already .. thanks :smile:


I'm so sorry :redface:
I should be more careful when reading...
Reply 82
Hoq many units are you guys doing¿
Coz like some people are already done m1,m1 and m3 ...
Original post by Killjoy-
I'm so sorry :redface:
I should be more careful when reading...


Dont worry about- still thanks for the help!! :smile:
I need all the help i can get
:smile:
Reply 84
Original post by avipsita
Hoq many units are you guys doing¿
Coz like some people are already done m1,m1 and m3 ...


I'll have done 12 maths units by the end of A2.

Already done 9 (C1, C2, C3, FP1, M1, M2, M3, D1, S1)

Doing C3, FP2 and S2 in the summer.
Reply 85
Original post by wibletg
I'll have done 12 maths units by the end of A2.

Already done 9 (C1, C2, C3, FP1, M1, M2, M3, D1, S1)

Doing C3, FP2 and S2 in the summer.


Almost the same units as me (doing FP3 instead of FP2.)
Reply 86
Original post by Killjoy-
Almost the same units as me (doing FP3 instead of FP2.)


Not bad :tongue: FP3 looks quite an odd module though?

How are you finding C4?
Could someone please help me with this q - put parametric eqs into a cartesian eq?

x = 3cost y = 9sin2t

The answer should be in the form y^2 = f(x)

The answer is 4x^2(9-x^2)

But I keep getting 36x^2(9 - x^2)

I get to this stage: y= 6x^2 (9-x^2)^1/2

and then when I square it, I get y = 36x^2 (9 - x^2)

Any help! :smile:
Reply 88
Original post by Phenylethylamine_
Could someone please help me with this q - put parametric eqs into a cartesian eq?

x = 3cost y = 9sin2t

The answer should be in the form y^2 = f(x)

The answer is 4x^2(9-x^2)

But I keep getting 36x^2(9 - x^2)

I get to this stage: y= 6x^2 (9-x^2)^1/2

and then when I square it, I get y = 36x^2 (9 - x^2)

Any help! :smile:


1) (x/3)^2 = (cost)^2
and (y/9) = 2sintcost so (y/18)^2 = (sint)^2(cost)^2

(y^2)/(18^2) = (1 - (cost)^2)(cost)^2 replace with equation 1)
y^2 = (18^2)( (x/3)^2 ) - (18^2)( (x/3)^2 )^2
y^2 = 36x^2 - 4x^4
y^2 = 4x^2(9 - x^2)
Original post by Antimony
1) (x/3)^2 = (cost)^2
and (y/9) = 2sintcost so (y/18)^2 = (sint)^2(cost)^2

(y^2)/(18^2) = (1 - (cost)^2)(cost)^2 replace with equation 1)
y^2 = (18^2)( (x/3)^2 ) - (18^2)( (x/3)^2 )^2
y^2 = 36x^2 - 4x^4
y^2 = 4x^2(9 - x^2)


Thank you! :smile:
Reply 90
Original post by wibletg
I'll have done 12 maths units by the end of A2.

Already done 9 (C1, C2, C3, FP1, M1, M2, M3, D1, S1)

Doing C3, FP2 and S2 in the summer.


Original post by Killjoy-
Almost the same units as me (doing FP3 instead of FP2.)

You two are hardcore :beard:

I need to go to sleep :frown: 8am start on C4 tomorrow.
Reply 91
hhaahha you guys are smart asses .. i am only going to have 9 units done buy the end to A2 level ...
Original post by Doctor.
You two are hardcore :beard:

I need to go to sleep :frown: 8am start on C4 tomorrow.


I'll have 14 :tongue:

C1, C2, C3, C4, S1, S2 as A-level maths (going by module marks, this is how they'd arrange them)
FP1, M1, D1 (AS) FP2, S3, D2 as A-level FM (I think my FP2 will be better than FP3)
FP3 and M2 left over - although FP3 might replace D2, or I might improve my M2 enough for it to go in FM.

Neglecting C4 for a bit at the moment to concentrate on learning FP3 and preparing for my first exam (C1).
Reply 93
Original post by Contrad!ction.
I'll have 14 :tongue:

C1, C2, C3, C4, S1, S2 as A-level maths (going by module marks, this is how they'd arrange them)
FP1, M1, D1 (AS) FP2, S3, D2 as A-level FM (I think my FP2 will be better than FP3)
FP3 and M2 left over - although FP3 might replace D2, or I might improve my M2 enough for it to go in FM.

Neglecting C4 for a bit at the moment to concentrate on learning FP3 and preparing for my first exam (C1).


Another one on the hardcore mathematics list :lol:

Now time for my mistakes :frown:. I did the chapter 8 misc questions, can't scan because...my scanner took a nasty fall :tongue:
-4
-7
-8

(C4 book misc questions 8, pages 343-344)
I don't really understand how to integrate them, I know it's got to do with logs etc? but I cant do it :frown:

Thanks guys :h:
Original post by Doctor.
Another one on the hardcore mathematics list :lol:

Now time for my mistakes :frown:. I did the chapter 8 misc questions, can't scan because...my scanner took a nasty fall :tongue:
-4
-7
-8

(C4 book misc questions 8, pages 343-344)
I don't really understand how to integrate them, I know it's got to do with logs etc? but I cant do it :frown:

Thanks guys :h:

:awesome:

I left my C4 book at school and we didn't do the miscs - what are the functions?
Reply 95
Original post by Contrad!ction.
:awesome:

I left my C4 book at school and we didn't do the miscs - what are the functions?


I just realised you're a mod :lol: Have I just not noticed all this time? :s-smilie:

4) find the general solution of the diff eq: dy/dx = x(y^2 +1) / (x-1)y

7) Obtain the general solution of the diff eq: y dy/dx tan2x = 1-y2

8) dy/dx = y^2 /x^2 - x -2
Reply 96
Original post by Contrad!ction.
I'll have 14 :tongue:

C1, C2, C3, C4, S1, S2 as A-level maths (going by module marks, this is how they'd arrange them)
FP1, M1, D1 (AS) FP2, S3, D2 as A-level FM (I think my FP2 will be better than FP3)
FP3 and M2 left over - although FP3 might replace D2, or I might improve my M2 enough for it to go in FM.

Neglecting C4 for a bit at the moment to concentrate on learning FP3 and preparing for my first exam (C1).


What year are you in blad?
Original post by Doctor.
I just realised you're a mod :lol: Have I just not noticed all this time? :s-smilie:

4) find the general solution of the diff eq: dy/dx = x(y^2 +1) / (x-1)y

7) Obtain the general solution of the diff eq: y dy/dx tan2x = 1-y2

8) dy/dx = y^2 /x^2 - x -2


I got it a couple of Thursdays ago, so it's actually quite recent :tongue:

Have you got to each integral? So (something) dy = (something else) dx ?

Original post by avipsita
What year are you in blad?

Year 13
Reply 98
Original post by Contrad!ction.
I got it a couple of Thursdays ago, so it's actually quite recent :tongue:

Have you got to each integral? So (something) dy = (something else) dx ?


Year 13


ah cool and well done :smile:

Yeah, it's the integrating I am a little stuck on.
Original post by Doctor.
ah cool and well done :smile:

Yeah, it's the integrating I am a little stuck on.

Got these?

yy2+1 dy=xx1 dx\displaystyle\int \dfrac{y}{y^2+1}\ dy = \int \dfrac{x}{x-1}\ dx

y1y2 dy=cot2x dx\displaystyle\int \dfrac{y}{1-y^2}\ dy = \int \cot 2x\ dx

For ln:
f(x)f(x) dx=ln(f(x))+k\displaystyle\int \dfrac{f'(x)}{f(x)}\ dx = ln(f(x)) + k
If there's a constant multiplying the differential, you'll need to deal with that as well.

For 8, could you use brackets to write it? I don't know whether the -x-2's on the denominator or not.
(edited 11 years ago)

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