# Mathematics: Post your doubts here!

#### Anum96

So we just have to put a minus sign in this situation ?!?
Oh no no. You're flipping the limits, right? So the sign will flip as well. Your negative sign will be changed to positive sign and so, You will get the correct transformation.

ohh ok !

#### Hassan Ali Abid

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!
Im trying to open the link but its not working for me ...anyways can you please have a look in to that book and lemm know if itcontains the probability using sets and venn diagrams

yeah please do search..it will surely be a great favour.

#### Hassan Ali Abid

Can anyone please explain me why the integration of (1/1+y^2) is tan inverse y and how the integration of y/1+y^2 gives .5ln(1+y^2) ???

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#### Anum96

View attachment 57680 Can anyone please explain me why the integration of (1/1+y^2) is tan inverse y and how the integration of y/1+y^2 gives .5ln(1+y^2) ???
Look. When you have a fraction. And you have to integrate it.
Consider the denominator. differentiate it. If your differentiated expression is the same as your numerator then you can simply use log to integrate. If not then see if you can make it the same by multiplying. For example. In the above case. Your denominator is
1+y^2
Now differentiate it and you will get 2y right? BUT you have only y in numerator. Therefore you will make them same by taking out 1/2 and then simply use log. I hope Im coherent enough for you to understand.
It will become 0.5ln(1+y^2)
If its still not clear then let me know I will try and explain via working step by step.

#### Anum96

A
View attachment 57680 Can anyone please explain me why the integration of (1/1+y^2) is tan inverse y and how the integration of y/1+y^2 gives .5ln(1+y^2) ???
Also. Is there any substitution given in the question?

#### Hassan Ali Abid

Look. When you have a fraction. And you have to integrate it.
Consider the denominator. differentiate it. If your differentiated expression is the same as your numerator then you can simply use log to integrate. If not then see if you can make it the same by multiplying. For example. In the above case. Your denominator is
1+y^2
Now differentiate it and you will get 2y right? BUT you have only y in numerator. Therefore you will make them same by taking out 1/2 and then simply use log. I hope Im coherent enough for you to understand.
It will become 0.5ln(1+y^2)
If its still not clear then let me know I will try and explain via working step by step.

Great ...yeah I have recalled and understood that part.Thanks for it ..but what about the first one ....are we suppose to use any substitution ???

#### Hassan Ali Abid

A

Also. Is there any substitution given in the question?
NO..nothing as such is given in the question.

#### bakhita

Im trying to open the link but its not working for me ...anyways can you please have a look in to that book and lemm know if itcontains the probability using sets and venn diagrams

yeah please do search..it will surely be a great favour.

For solved past papers, I did search, but they really aren't available online yet...A few sites are updating solved papers, but as I told you, there really is no chance for S2,...I found solved ones for Mechanics, and many other subjects, but no Statistics ....

Probability using venn diagram is explained in the book, but that's only for understanding of 'combined events' and mutually exclusive events etc, but there is no practice for these...it would be better if you have a look at the book yourself... the link doesn't work? works fine for me though..okay try to open this:
http://www.aliensservices.com/A_Level_Books.html

#### Hassan Ali Abid

For solved past papers, I did search, but they really aren't available online yet...A few sites are updating solved papers, but as I told you, there really is no chance for S2,...I found solved ones for Mechanics, and many other subjects, but no Statistics ....

Probability using venn diagram is explained in the book, but that's only for understanding of 'combined events' and mutually exclusive events etc, but there is no practice for these...it would be better if you have a look at the book yourself... the link doesn't work? works fine for me though..okay try to open this:
http://www.aliensservices.com/A_Level_Books.html

Then isnt there any other book having explaining everything with solved/worked examples ??

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#### Anum96

NO..nothing as such is given in the question.
No. It wouldve been easier with a substitution though.
But The reason is that d(arctan x)/dx = 1/(1+x^2)

and the integral is the opposite of the derivative

#### Hassan Ali Abid

No. It wouldve been easier with a substitution though.
But The reason is that d(arctan x)/dx = 1/(1+x^2)

and the integral is the opposite of the derivative

but how is it possible to solve that with substitution ? and which substitution will be used?

#### Anum96

NO..nothing as such is given in the question.
Its not possible without substitution. Take substitution y = tanx or no. I dont understand it

Tbh Ive never been more baffled.

#### Anum96

but how is it possible to solve that with substitution ? and which substitution will be used?
If you applied the correct identity it might help . . . tan2(x)+1=sec2(x) Your integral equation then becomes, ∫1x2+1dx=∫dθ

^^This is what a teacher said.

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