P2 / P3 question of Integration Watch

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AngelofnoColour
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Im doing P3, P1 and S1 next week.

How do you integrate 8/ x^2 + 1 ????

Can you integrate where the denominator has a power???

Please help, thanx.
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Morgan
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Is that 8 / (x^2 + 1) or (8 / x^2) + 1 ?
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kikzen
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(Original post by BlueAngel)
Im doing P3, P1 and S1 next week.

How do you integrate 8/ x^2 + 1 ????

Can you integrate where the denominator has a power???

Please help, thanx.
you need to specify what is the denominator.

i suspect its (x^2 + 1) thats the total denominator (if it was just x^2, thats p1)

there are several ways to do it, but the easiest is to look in the formula book other wise, some sort of substitution will do it.
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AngelofnoColour
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(Original post by Morgan)
Is that 8 / (x^2 + 1) or (8 / x^2) + 1 ?
Its 8 / (x^2 + 1)

Actually this is more difficult, its in the P3 exam paper.


Evaluate this Limits are x = square root of 2 and x = 0

Integral of x / squareroot of (16 - x^4) -


Ive got the answers, just doesnt explain it.
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Ralfskini
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(Original post by BlueAngel)
Im doing P3, P1 and S1 next week.

How do you integrate 8/ x^2 + 1 ????

Can you integrate where the denominator has a power???

Please help, thanx.

Let x=tanu
dx=sec^2u.du

int.8/x^2+1.dx=8int.sec^2u/sec^2u.du=8u+C=8arctanx+C.
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Morgan
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(Original post by BlueAngel)
Its 8 / (x^2 + 1)

Actually this is more difficult, its in the P3 exam paper.


Evaluate this Limits are x = square root of 2 and x = 0

Integral of x / squareroot of (16 - x^4) -


Ive got the answers, just doesnt explain it.
Okay you can just substitute and use u = x^2 +1 I think and glancing at the second one I think its a nominator-derivative of the denominator one.
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AngelofnoColour
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(Original post by Ralfskini)
Let x=tanu
dx=sec^2u.du

int.8/x^2+1.dx=8int.sec^2u/sec^2u.du=8u+C=8arctanx+C.

OK RALFSKINI PLEASE TELL ME WHY YOU WOULD USE TAN HAS A SUBSTITUTION WHEN THE EQUATION INVOLVES ONLY NUMBERS, COS I AM SO CONFUSED NOW
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A0307
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(Original post by BlueAngel)
Im doing P3, P1 and S1 next week.

How do you integrate 8/ x^2 + 1 ????

Can you integrate where the denominator has a power???

Please help, thanx.
The derivtative of tan^-1(x) is a standard form and is 1/(x^2 + 1).

Using this, it's simply 8tan^-1x + C.

The standard form is INT c/(ax^2 + b^2) = c.tan^-1(x/b)
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AngelofnoColour
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(Original post by calumc)
The derivtative of tan^-1(x) is a standard form and is 1/(x^2 + 1).

Using this, it's simply 8tan^-1x + C.

The standard form is INT c/(ax^2 + b^2) = c.tan^-1(x/b)



Is this from P3??
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Ralfskini
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(Original post by BlueAngel)
OK RALFSKINI PLEASE TELL ME WHY YOU WOULD USE TAN HAS A SUBSTITUTION WHEN THE EQUATION INVOLVES ONLY NUMBERS, COS I AM SO CONFUSED NOW

You can make this substitution because of the trig identity- 1+tan^x=sec^2x.
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tammypotato
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how do u guess wot to use for u in subtitution?
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A0307
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(Original post by BlueAngel)
Is this from P3??
I have no idea, I did Advanced Highers which are slightly different, and harder apparently.
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Silly Sally
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(Original post by Ralfskini)
Let x=tanu
dx=sec^2u.du

int.8/x^2+1.dx=8int.sec^2u/sec^2u.du=8u+C=8arctanx+C.
being able to get arctan from an integration isn't on P3!!!

Can someone please tell me how to do this question - cos it's getting me worried
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Ralfskini
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(Original post by Silly Sally)
being able to get arctan from an integration isn't on P3!!!

Can someone please tell me how to do this question - cos it's getting me worried

..but I have only done up to P3. :confused:
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Silly Sally
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(Original post by Ralfskini)
..but I have only done up to P3. :confused:
Do you do edexcel or another board?
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Ralfskini
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(Original post by Silly Sally)
Do you do edexcel or another board?

Edexcel.
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Silly Sally
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(Original post by Ralfskini)
Edexcel.
AGHHHHH!! Same as me!!!! I can't do this integration. I would at first have involved an 'ln', like integral of 1/(3x + 1) = 1/3 ln (3x +1) <--- i think - now i don't know whther this is right or wrong!!!
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Ralfskini
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(Original post by Silly Sally)
AGHHHHH!! Same as me!!!! I can't do this integration. I would at first have involved an 'ln', like integral of 1/(3x + 1) = 1/3 ln (3x +1) <--- i think - now i don't know whther this is right or wrong!!!

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