More integration….

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Heixi
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#1
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#1
I need to get 1+….
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Heixi
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#2
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#2
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mqb2766
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#3
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#3
What did you do for the denominator? Also -2 on the numerator? Also limits?

Note again, the easier way to do the dx -> du is
dx/du = 2u
so
dx -> 2u du
Last edited by mqb2766; 5 months ago
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Heixi
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#4
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#4
(Original post by mqb2766)
What did you do for the denominator?
I didn’t do anything
I differentiated the substitution to get (rootx-2)-1
But if I subbed that back into the integral I wouldn’t get 1+ Root x-2 only 3-x/root x-2
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mqb2766
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#5
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#5
(Original post by Heixi)
I didn’t do anything
I differentiated the substitution to get (rootx-2)-1
But if I subbed that back into the integral I wouldn’t get 1+ Root x-2 only 3-x/root x-2
You should have u+1 on the denominator.
I don't follow what youre saying here.
Last edited by mqb2766; 5 months ago
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Heixi
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#6
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#6
(Original post by mqb2766)
You should have u+1 on the denominator.
I don't follow what youre saying here.
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mqb2766
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#7
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#7
(Original post by Heixi)
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The denominator is 1+sqrt(x-2). You can't just split off the sqrt(x-2) part.

u/(u+1) is not 1.
Last edited by mqb2766; 5 months ago
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Heixi
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#8
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#8
(Original post by mqb2766)
The denominator is 1+sqrt(x-2). You can't just "cancel" the sqrt(x-2) part.

u/(u+1) is not 1.
I didn’t try to cancel it , I left it blank but anyways Name:  4B5988E3-BE4B-44AB-B97B-6AAF62ED8B4E.jpeg
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mqb2766
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#9
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#9
(Original post by Heixi)
I didn’t try to cancel it , I left it blank but anyways Name:  4B5988E3-BE4B-44AB-B97B-6AAF62ED8B4E.jpeg
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The +2 on the numerator is -2 and you have an extra u when you do the
dx -> 2u du
substitution.

The "cancel" referred to the fact that
dx -> 2u du
and you had
1+u
on the denominator. You said
u /(1+u) du = du
hence the "cancel".
Last edited by mqb2766; 5 months ago
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mqb2766
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#10
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#10
(Original post by Heixi)
I get what you mean but how would I get that 1+
WHat do you think the denominator of the original function is in terms of x?
Write down clearly how it transforms to u.
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Heixi
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#11
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#11
(Original post by mqb2766)
WHat do you think the denominator of the original function is in terms of x?
Write down clearly how it transforms to u.
I’m stuck on the denominator
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mqb2766
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#12
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#12
(Original post by Heixi)
I’m stuck on the denominator
How? You start with
1 + sqrt(x-2)
In terms of u it is ...
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Heixi
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#13
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#13
(Original post by mqb2766)
How? You start with
1 + sqrt(x-2)
In terms of u it is ...
That’s just U+1
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mqb2766
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#14
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#14
(Original post by Heixi)
That’s just U+1
Yes.
So replace dx with the corresponding expression in terms of u and du, and modify the limits so they're in terms of u.

I can't help thinking you;re overcomplicating it at the start by not saying dx/du = 2u directly, then simply doing the substitution for each part, then cancelling if necessary.
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Heixi
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#15
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#15
(Original post by mqb2766)
Yes.
So replace dx with the corresponding expression in terms of u and du, and modify the limits so they're in terms of u.

I can't help thinking you;re overcomplicating it at the start by not saying dx/du = 2u directly, then simply doing the substitution for each part, then cancelling if necessary.
This is really not working out for me
I need to get 3-u^2+2/U+1
I’m getting 3-u^2+2/2U
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mqb2766
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#16
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#16
(Original post by Heixi)
This is really not working out for me
I need to get 3-u^2+2/U+1
I’m getting 3-u^2+2/2U
Can you clearly show your working when you substitute for u in the
* numerator,
* denominator
* dx
and then any simplifcation when you put them together with the transformed limits.

What you "need to get" is wrong. But so is what youre currently gettting.
Last edited by mqb2766; 5 months ago
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Heixi
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#17
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#17
(Original post by mqb2766)
Can you clearly show your working when you substitute for u in the
* numerator,
* denominator
* dx
and then any simplifcation when you put them together with the transformed limits.

What you "need to get" is wrong. But so is what youre currently gettting.
Maths is really not for me . At this point I’m just making stuff up
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mqb2766
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#18
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#18
Youre not doing it clearly. For the numerator
3 - x = 3 - (u^2 + 2) = 1 - u^2
The 2 on the numerator is subtracted if you write it down clearly. You had it as +2.

As above (several times)
dx = 2u du
You arguably complicate it by expressing u = sqrt(...) then differentiating to get du/dx in terms of x and then trying to manipulate more complex expressions in x.

As above, the denominator is
u+1

Simply put the three things together with the transformed limits and see if you can simplify then integrate.
Last edited by mqb2766; 5 months ago
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Heixi
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#19
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#19
(Original post by mqb2766)
Youre not doing it clearly. For the numerator
3 - x = 3 - (u^2 + 2) = 1 - u^2
The 2 on the numerator is subtracted if you write it down clearly. You had it as +2.

As above (several times)
dx = 2u du
You arguably complicate it by expressing u = sqrt(...) then differentiating to get dx/du in terms of x and then trying to manipulate more complex expressions in x.

As above, the denominator is
u+1

Simply put the three things together with the transformed limits and see if you can simplify then integrate.
I am infuriating…
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mqb2766
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#20
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#20
(Original post by Heixi)
I am infuriating…
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The final expression is correct, but I would have left it written as a fraction (numerator and denominator) then think if the numerator can be factorized to cancel the denominator. Then integrate with the transformed limits.
Last edited by mqb2766; 5 months ago
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