i post up the solution, you explain alright x)
sorry arh, the question abit different.
step 2 i dont understand.




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Intergration must expand it wad..
U dun expand cant do..

nvm

This post has been edited by Leto Kynes: Nov 2 2008, 11:50 PM

This is the integration I've been wanting to know how to do.
Any experts?

OMG! I had a bad time typing equations in microsoft word... just so mafan and hard to type. Someone guide me with it!

Anyways, I hope the solution below is correct.

PS: Your recent posted image is not the same as the one you give initially. The 2nd one is definite integration... this one is indefinite.

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Added on November 3, 2008, 12:37 am@Shenay,

I'm not getting the same answer as the solution posted btw... for step 2 I get:

2 [ (x^2 - x^3) / ( 3(1-3x) ) ]

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Added on November 3, 2008, 12:45 amNot necessary, if the equation is up to a power of 3 and more how are you going to expand? It's going to be a hella long to do that.

there is a formula for this particular case.

This post has been edited by Zepx: Nov 3 2008, 12:45 AM


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Try expanding it first then only integrate.

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Added on November 3, 2008, 12:54 amDidn't know you could do that. So you treat the stuff in the bracket as one whole term?

This post has been edited by raptor_cZn: Nov 3 2008, 12:54 AM

I don't think you can do that
Lets say integrate 2x-3x²

Your method
2x-3x²
= x(2-3x)
= (x²/2)(2x- 3x²/2)
= x³ - 3x⁴/4

Correct method
2x-3x²
= x² - x³

I didn't get x³ - 3x⁴/4

instead i get x² - x³

You can directly integrate the x² - x³

and no, you cannot remove x as a common factor. why? because you are integrating dx. if you do that, meaning x is take out of the integration, in the end, you still have x.


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raptor_cZn,

You can try expanding the equation and then integrate it. It comes to the same as mine. And yes, it's under our syllabus to take the whole bracket as one whole thing and integrate it. Alternatively, you represent

1-3x = u
1/u²

or something like tat.

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Added on November 3, 2008, 6:56 amOh ya, to add,

for thins like

(3-1x)³

there is a formula for this.

(ax-b)ⁿ⁺¹ / (dy(ax-b)/dx * n+1)

Meaning, I should get:

(3-1x)⁴/(-1 * 4)
(3-1x)⁴/-4

Please check your book in reference to this. I'm not using anything out of syllabus.

This post has been edited by Zepx: Nov 3 2008, 06:56 AM

why need to factorise to make ur life harder leh =_=
just intergrate the simple equation?
i think hot choc get it right

Zzz.... please read my equations closely. Since when did I factorise the x out? I'm doing the normal way.

Either way, from my friends, point of view, there is no solution for this equation. It is not possible to integrate as the combination of nominator and denominator especially when the denominator is powered by 2.

What I meant was, you seperated it out.
So, I did the same with another example.

Your Solution
(2x-3x²)/(1-3x)²
= (2x-3x²)(1-3x)^-2 (Here you make it into multiply)
= (x²-x³)[(1-3x)^-1/3] (Here you differentiated separately.)

My example
2x-3x²
= x(2-3x) (Here I factorise it, also means i make it into multiply)
= (x²/2)(2x- 3x²/2) (Here I differentiated separately)
= x³ - 3x⁴/4 (Here my answer is wrong.)

got admaths question that needs to be solved.

The velocity, v of a particle which moves along a straight line, t seconds after passing a fixed point O, is given by v=10t-3t²+8. Find the interval from the instant the particle starts until it is instantaneously at rest.

pwincess, is the answer 4s ?

yep. how did u do it?
can u show the calculation ?

okie you see ya, when there's this word, "instantaneously at rest" means v=0. cause at rest velocity is zero. take the V equation, and equate it to zero.

v= 10t-3t2+8 = 0, and then factorize and get two answers.
you will get -3/2 and 4. since its time, so yeah the first answer is not accepted =)

i c. thx for the explaination ! ;D

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Added on November 3, 2008, 2:29 pmbtw, how to score high marks on bm and english essay ?

This post has been edited by pwincess: Nov 3 2008, 02:29 PM

I suspect there is a proving question on differentiation before doing this integration. Or else, straight-away integration for this expression is beyond SPM level.

Mind posting the proving question? It helps a lot for this question.

haha ken, yes i got it already ><
its a proving question.
but i was just wondering is there, a way to intergrate without proving =)

Hello

i just want to ask
is there any way to intergrate this??


3x²+2x+15
--------------
(1+3x)²

I have literally banged my head on this. The expression is integratable, only with technique beyond SPM. Even so, the upper and lower limits cannot fit into the integration.

In short, no straight-away integration for this question.


Feel the horror of mathematics! MUAHAHAHAHA

It's beyond SPM level.