# Mathematics: Post your doubts here!

#### Anum96

in part ii i am stuck at this step ..
Use the substitution now

ʃ5sin^3x*cos^2x dx

You have dx and u substitution

= ʃ 5sin^3x(u^2) (du/-sinx)

Cancelling out will give you,

=ʃ-5sin^2x(u^2)

Use trig identity : sin^2x = 1 – cos^2x

=-ʃ5(1 – cos^2x)(u^2)du

=-5ʃ(1 – u^2)(u^2)du

= -5ʃu^2 – u^4 du

=- 5 [(u^3/3) – (u^5/5)]

Put limits in.

-5 {[(1/3 – 1/5) – (0/3 – 0/5)]}

= -5 (2/15)

= -10/15

= -2/3

Area = 2/3 Ans.
*I think I messed up a sign somewhere or its the way it is

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thanks !

#### Hassan Ali Abid

I'm using this book :
covers both S1 and S2
As for pastpapers, when I bought solved past papers, I had chosen S1 and M1 but later I changed my mind and found Statistics much more bearable than Mechanics, so I've solved papers for S1 but not for S2..But it doesn't matter, I'll print out unsolved ones and I can check them through mark schemes! What's your plan?
So aren't you having this book in pdf form or is it available for free online ?
Are there any solved papers for S2 ??? ...if you have them then i need them urgently.
I have tried to use to use ms for S2 but it didnt work out for me bcz the method is not given in the ms :/

#### Hassan Ali Abid

I'm using this book :
covers both S1 and S2
As for pastpapers, when I bought solved past papers, I had chosen S1 and M1 but later I changed my mind and found Statistics much more bearable than Mechanics, so I've solved papers for S1 but not for S2..But it doesn't matter, I'll print out unsolved ones and I can check them through mark schemes! What's your plan?
and one thing more ...does that book contains the topics such as cdf ,pdf , chi square etc ???

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#### Anum96

Use this. Pretty similar example

#### bakhita

So aren't you having this book in pdf form or is it available for free online ?
Are there any solved papers for S2 ??? ...if you have them then i need them urgently.
I have tried to use to use ms for S2 but it didnt work out for me bcz the method is not given in the ms :/
Yes, the book is available online, check this website:
http://www.aliensservices.com/E-books.html

As for the solved papers, it's difficult, a mere chance, that they'll be available for S2, very few students choose S2, but I'll search and let you know if I find!

#### bakhita

and one this more ...does that book contains the topics such as cdf ,pdf , chi square etc ???
Yes, it does cover these, the probability density function and cumulative distribution function are covered in 6th unit, chi square must be there too and I can assure you, it covers ALL of the syllabus, and even more than that, soyou must keep checking the syllabus, like there is the one "Regression and Corrlation", that I haven't really found in syllabus so I skipped that.

#### Wolfgangs

Can someone tell me the final answer and working for this question please?

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#### Anum96

Can someone tell me the final answer and working for this question please?
You should post this in some physics thread. Your previous questions were related to mechanics. That's why I could help. I don't know physics

#### Sarosh Jameel

plz help the answer i am getting is 1 / -y ( 1+y )

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#### Anum96

plz help the answer i am getting is 1 / -y ( 1+y )
Yes, Im getting the same. I believe we are not wrong. There must be a problem with the question. Which year is it?

#### Sarosh Jameel

yeah !! i am searching for the paper year !! i will tell u

#### Anum96

yeah !! i am searching for the paper year !! i will tell u
Okay. Waiting

#### Sarosh Jameel

yeah !! i am searching for the paper year !! i will tell u
couldn't find .. i hope our answers are correct !

#### Anum96

couldn't find .. i hope our answers are correct !
Listen. We are wrong. Why? because if you take note of your solution. You get the limit 1 when x is zero. and limit 0.5 when x is ln2. Observe how the position changes of both the values. Before transformation we have ln2 as the larger limit but when we calcute y we get 1/2 which is the smaller value in the transformation. Therefore, When this happens, The sign of the expression can change

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#### Sarosh Jameel

Listen. We are wrong. Why? because if you take note of your solution. You get the limit 1 when x is zero. and limit 0.5 when x is ln2. Observe how the position changes of both the values. Before transformation we have ln2 as the larger limit but when we calcute y we get 1/2 which is the smaller value in the transformation. Therefore, When this happens, The sign of the expression can change