2007 HSC Maths Ext2 UnOfficial Discussion Thread (1 Viewer)

[Hikari Clover]

c'mon guys,post up ur feeling here~~~

only 1 week to go ,so scared.......

:wave:

 

[Kujah]

Good luck :wave:

 

[aljoz]

Dont really give a damn LOL. ill study a bit for it........but meh.. im over HSC; just get the exam over and done with ...

 

[kony]

confirmed questions:

integrate xtanx and e^(x²)

good luck guys.

 

[Trebla]

confirmed questions:

integrate xtanx and e^(x²)

There is no explicit formula for the integral of e^x². In fact no explicit formula exists at the moment (at least none that I've heard of) for xⁿe^x² whenever n is an even number or zero...lol

 

[kony]

how about n=1, integrate xe<sup>x²


</sup>

 

[Yip]

A more plausible version of kony's question is integrate e^(-x²) from 0 to infinity, which does have a very nice closed form answer. A slightly more nasty version would be to integrate (x^n)[e^(-x²)] from 0 to infinity, where n is a positive integer. Another nice q is to show that the integral sinx/x from 0 to infinity is pi/2.

 

[FromDeeEast]

^ wow fuck u, now i dont feel so confident :S

 

[lilfrenchi]

A more plausible version of kony's question is integrate e^(x²) from 0 to infinity, which does have a very nice closed form answer. A slightly more nasty version would be to integrate (x^n)[e^(x²)] from 0 to infinity, where n is a positive integer. Another nice q is to show that the integral sinx/x from 0 to infinity is pi/2.

how do u do that??

 

[Hikari Clover]

回复: Re: 2007 HSC Maths Ext2 UnOfficial Discussion Thread

how do u integrate xtanx ????

 

[bos1234]

only 3 now.... qn 1-5 are ok..
then its downhill from there for me...
and harder 3 unit hopefully i can get at least half a qn right if that... :S

 

[Golbez]

Re: 回复: Re: 2007 HSC Maths Ext2 UnOfficial Discussion Thread

xtan(x) would involve recurrance wouldn't it?

correct me if I'm wrong anywhere here...

IBP-

let

u = tan (x) v' = x
u' = sec^2 (x) v = 1/2 x^2

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

Using IBP again...

u = x^2 v' = sec^2 (x)
u' = 2x v = tan (x)

Int (x * tan (x) ) = 1/2 (x^2 * tan (x)) - x^2 * tan (x) + 2 Int (x * tan (x))

Take 2 Int ( x * tan (x) ) from both sides

-Int (x * tan(x) ) = 3/2 (x^2 * tan (x))

Int (x * tan(x) ) = -3/2 (x^2 * tan (x))

 

[kony]

there is no 2I on the RHS in your last few lines of working. it's actually just I. (there's a 1/2 right at the front which cancels the 2)

 

[Starcraftmazter]

c'mon guys,post up ur feeling here~~~

How am I feeling...kinda like this;

Anyway, should be survivable, as long as we follow the rules.

 

[Yip]

Just to clear up some confusion, the indefinite integral of xtanx has no answer expressible in terms of simple functions. Golbez's approach was not correct, in the second IBP, he was simply reversing what he did in the first IBP, which results in the rather useless equality I=I. The integrals I posted earlier are also sort of beyond 4u if just asked outright, though they may be fair game if given appropriate lead up.

 

[Hikari Clover]

回复: Re: 2007 HSC Maths Ext2 UnOfficial Discussion Thread

.........
i cant integrate xe^x² as well..........

 

[Starcraftmazter]

Re: 回复: Re: 2007 HSC Maths Ext2 UnOfficial Discussion Thread

.........
i cant integrate xe^x² as well..........

What's so special about it? The answer is 1/2 . e^x^2 + c, very simple :S