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integration help (1 Viewer)

Timothy.Siu

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3unitz said:
Int x. [root(x+1)] dx

dx = 2u du
u = root(x+1)

Int [(u^2)-1]. u 2u du

Int 2u^3 - 2u^2 du

u^4/2 - 2u^3/3 + C

(x+1)^2/2 - 2(x+1)^(3/2)/3 + C
made a mistake on the third last line shud be 2u^4
 

P.T.F.E

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y bdw caps lock didnt mean i was being a smart ass, i was mearly pointing that out, bdw what is the answer!!! y havnt i finished the q it asked to intergrate that is what i did. i was havin a go at it
 

Timothy.Siu

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P.T.F.E said:
y bdw caps lock didnt mean i was being a smart ass, i was mearly pointing that out, bdw what is the answer!!! y havnt i finished the q it asked to intergrate that is what i did. i was havin a go at it
because u left it in terms of u, and secondly its wrong anyway.
 

lyounamu

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Just follow the freaking question.

You do that and you will get it wrong. When people post up question, they are more interested in the solution than answer.

x = u^2 -1
dx/du = 2u

x sqrt(x+1) dx = (u^2-1)u dx
= (u^2-1)u . 2u du
= 2u^4 - 2u^2 du

Integrate so you get:
2u^5/5 - 2u^3/3 + c

But u^2 = x+1
so u^5 = (x+1)^2.5
and u^3 = (x+1)^1.5

so

answer = 2(x+1)^2.5/5 - 2(x+1)^1.5/3 + c

you will obviously see that using x = u^2 -1 isn't much harder. It's like easier.
 

P.T.F.E

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pfft dont care i made a mistake woop woop so did u smart arse. its a first for me mistakes are unusual to me but when u have been doin econmics all day bound to happen!!!
 

shaon0

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P.T.F.E said:
pfft dont care i made a mistake woop woop so did u smart arse. its a first for me mistakes are unusual to me but when u have been doin econmics all day bound to happen!!!
You should stop lying. It's a bad habit.
 

lyounamu

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It would be more annoying to see fight between a boy and a girl.
 

Continuum

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Namu, do you know if there's a difference between the reverse chain rule and integration by substitution ? :(
 

lyounamu

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Continuum said:
Namu, do you know if there's a difference between the reverse chain rule and integration by substitution ? :(
Reverse chain rule?

Haven't heard such a thing. Sorry for the lack of info.
 

Pwnage101

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Continuum said:
Namu, do you know if there's a difference between the reverse chain rule and integration by substitution ? :(
i'm not namu, but can i answer the Q? lol

well they are basically the same

ull neva be asked to 'use the reveers chain rule

but basically, with the reverse chain rule technically u do use a substitution in ur head, but when u sub in du it turns out 'nicely' ie:

INT (sinxcosx).dx

now u could use a substituion like u=sinx, but by using 'the reverse chain rule' u notice that this will yield an answer that is (1/2)(sinx)^2 + C - ie when u sub in du=cosx.dx it turns out as INT u.du, which is a very simple function, so technically they are the same thing - we call it 'ther reverse chain rule' because when u derive something via teh chain rule, u multiply teh function by it';s derivative at the end, and so if we have an integration with a function multiplied by its derivatrive, its sorta the revers, and that derivcative disappears

if u dont get it, just use a substitution, its the SAME THING, ur just doing more owrking out on the page, which is a good thing!

BUT dont worry about it

if u do 4U u'll get the hang of things and itll be much smoother in the integration chapter
 
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