Mathematics: Post your doubts here!

[LMGD33]

Please HELP!!
Hey can any1 tell me hw to integrate 4x/(4+x^2) ?

Thank u!!
SararaIH
PhyZac .... or any1?

Hello! following the rule where S denotes integration
S f ' (x) / f (x) = ln |f(x) | + c
You realize that 4 + x^2 differentiated is 2x
Now to make the numerator 2x, you simply divide by 2 so 4x/2 = 2x
Now you can integrate to : 1/2 ln (4 + x^2)

 

[Ashique]

Please HELP!!
Hey can any1 tell me hw to integrate 4x/(4+x^2) ?

Thank u!!
SararaIH
PhyZac .... or any1?

Use partial fractions first, then integrate.

 

[SararaIH]

Please HELP!!
Hey can any1 tell me hw to integrate 4x/(4+x^2) ?

Thank u!!
SararaIH
PhyZac .... or any1?

let S be the integration sign
Use this formula: S 1/(x^2+a^2) dx = (1/a)*tan^-1(x/a)

So it will be,

(1/2)*tan^-1(x/2)

I think... :/ I'm not sure though
What's the answer?

 

[Ashique]

This is how I like to present it..

I don't see the photo. Could you please repost it? Really appreciate the help!

 

[Anika Raisa]

Use partial fractions first, then integrate.

hw cn i do partial fraction will i have to break (4+x^2) into two n then....
Thank u!

 

[Anika Raisa]

let S be the integration sign
Use this formula: S 1/(x^2+a^2) dx = (1/a)*tan^-1(x/a)

So it will be,

(1/2)*tan^-1(x/2)

I think... :/ I'm not sure though
What's the answer?

Its part of on 11 31 q 8 ii ....

 

[fathimaash]

Hey ppl. R we provided with the formula sheet for tomorrow's ppr?? Thanks in advance.

 

[Rutzaba]

Please HELP!!
Hey can any1 tell me hw to integrate 4x/(4+x^2) ?

Thank u!!
SararaIH
PhyZac .... or any1?

the rule is that if fx = function
and f' x = its differential
then the integral of f'x/fx = ln fx+c
the differential of 4+x^2 is 2x
so we take 2 common and make the eq
2 integral of 2x/ 4 +x^2
2 ln 4+x^2
hope u got it

 

[Ashique]

Guys plz help me out in the last three questions of this paper: http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w12_qp_32.pdf

Honestly, this was the HARDEST paper ever! The threshold for an A was 47/75! How crazy is that?

 

[Anika Raisa]

Hello! following the rule where S denotes integration
S f ' (x) / f (x) = ln |f(x) | + c
You realize that 4 + x^2 differentiated is 2x
Now to make the numerator 2x, you simply divide by 2 so 4x/2 = 2x
Now you can integrate to : 1/2 ln (4 + x^2)

actuali may be i typed wrong its 4x/(4+x^2) !! Sorry!!! Thnk u!

 

[Rutzaba]

Hey any one know how to do no. 7iii here :
http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_w11_qp_31.pdf .... (Cud do i n ii bt not iii )

Here is wat i hv done in iii:

View attachment 26713

Please Help!! Thank u!!!

littlecloud11 Rutzaba PhyZac
VampBhums or any1?

First we would make the eq of line AB
We find b1 = OB-OA
(3,4,0) - (1,2,2) = (2,2,-2)
Line of eq AB = r +tb1
Where t is the constant given as alpha in the question
And r is any one point on the line. Lets take OA
(1,2,2) +t (2, 2, -2) ---------- eq of line AB
Any point on line ab will have points
(1+2t), (2+2t),(2-2t) we shall take this to be the point P
Now to find cos AOP we will have two points OP and OA
(OA) . (OP) = | OA | |OP | cos AOB
Where mod of OA= root of ( 1^2 +2^2+2^2) = 3
And mod of OP= root of ((1+2t) ^2 + (2+2t) ^2+(2-2t) ^2) = (√ 12t^2 +4t+9)
We have (1,2,2). ((1+2t), (2+2t),(2-2t) ) = (√9) (√ 12t^2 +4t+9) cos AOB
1+2t + 4+4t +4-4t = 3 (√ 12t^2 +4t+9) cos AOB
9+2t = 3(√ 12t^2 +4t+9) cos AOB
9+2t / 3(√ 12t^2 +4t+9) = cos AOB ---- I
Then we come to BOP
(OB) .(OP) = | OB | |OP | cos BOP
(3,4,0) . ((1+2t), (2+2t),(2-2t) ) = (√25) (√ 12t^2 +4t+9) cos BOP
14t +11 /5 (√ 12t^2 +4t+9) =cos BOP
Both (√ 12t^2 +4t+9) cancelled
We have
14t +11/ 5 = 9+2t / 3
42t +33 = 45 +10t
32t= 12
T= 3/8

 

[SararaIH]

the rule is that if fx = function
and f' x = its differential
then the integral of f'x/fx = ln fx+c
the differential of 4+x^2 is 2x
so we take 2 common and make the eq
2 integral of 2x/ 4 +x^2
2 ln 4+x^2
hope u got it

Thank you so much! I was confused with this as well!

 

[SararaIH]

Hey everyone,
I know that there is a saying that you shouldn't work too much or put too much pressure on yourself before the day of your exam. But can anyone give me some tips and advice about what I should do before the day of the exam? Like revision methods or revision styles that should follow? Or what papers I should solve before the day of the exam?

 

[waver525]

Hey everyone,
I know that there is a saying that you shouldn't work too much or put too much pressure on yourself before the day of your exam. But can anyone give me some tips and advice about what I should do before the day of the exam? Like revision methods or revision styles that should follow? Or what papers I should solve before the day of the exam?

try the 2012 ones they will be gud practice..

 

[Anika Raisa]

First we would make the eq of line AB
We find b1 = OB-OA
(3,4,0) - (1,2,2) = (2,2,-2)
Line of eq AB = r +tb1
Where t is the constant given as alpha in the question
And r is any one point on the line. Lets take OA
(1,2,2) +t (2, 2, -2) ---------- eq of line AB
Any point on line ab will have points
(1+2t), (2+2t),(2-2t) we shall take this to be the point P
Now to find cos AOP we will have two points OP and OA
(OA) . (OP) = | OA | |OP | cos AOB
Where mod of OA= root of ( 1^2 +2^2+2^2) = 3
And mod of OP= root of ((1+2t) ^2 + (2+2t) ^2+(2-2t) ^2) = (√ 12t^2 +4t+9)
We have (1,2,2). ((1+2t), (2+2t),(2-2t) ) = (√9) (√ 12t^2 +4t+9) cos AOB
1+2t + 4+4t +4-4t = 3 (√ 12t^2 +4t+9) cos AOB
9+2t = 3(√ 12t^2 +4t+9) cos AOB
9+2t / 3(√ 12t^2 +4t+9) = cos AOB ---- I
Then we come to BOP
(OB) .(OP) = | OB | |OP | cos BOP
(3,4,0) . ((1+2t), (2+2t),(2-2t) ) = (√25) (√ 12t^2 +4t+9) cos BOP
14t +11 /5 (√ 12t^2 +4t+9) =cos BOP
Both (√ 12t^2 +4t+9) cancelled
We have
14t +11/ 5 = 9+2t / 3
42t +33 = 45 +10t
32t= 12
T= 3/8

Thank u!
But 7 iii has only 1 mark do we need dat much detail! Besides ur ans doesnt prove
cz AP: OB=3:5 !!!
its just OA:OB!!!

 

[waver525]

pls can any one help me in q 10 part ii of the paper...... I believe this q is only one of its kind till now..

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_w10_qp_33.pdf
http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_w10_ms_33.pdf

 

[Rutzaba]

Thank u!
But 7 iii has only 1 mark do we need dat much detail! Besides ur ans doesnt prove
cz AP: OB=3:5 !!!
its just OA:OB!!!

y dun u open the question... i havent even done part three xD
this is part two

 

[Anika Raisa]

y dun u open the question... i havent even done part three xD
this is part two

oh ryt u did ii ! Sorry i m really lost 2day preperin 4 chem wid P3! Btwn i cud do dat bt not part iii Cud u pls help with dat part please!!!

 

[Anika Raisa]

y dun u open the question... i havent even done part three xD
this is part two

oh ryt u did ii ! Sorry i m really lost 2day preperin 4 chem wid P3! Btwn i cud do dat bt not part iii Cud u pls help with dat part please!!!

 

[SararaIH]

try the 2012 ones they will be gud practice..

I was afraid someone would say that
But the 2012 papers are the hardest
And do you think it's a good idea to lower your confidence before the exams?