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A level maths integration help!!!!!!

I got -1/2 instead of -1/4, due to there being an extra x2
The link to the answer is here:https://imgur.com/gallery/UJIcLIW
Can someone explain why there is an extra x2???

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Original post by PeaceMinusOne
I got -1/2 instead of -1/4, due to there being an extra x2
The link to the answer is here:https://imgur.com/gallery/UJIcLIW
Can someone explain why there is an extra x2???

Can I see your working, and the original question please?
Original post by PeaceMinusOne
I got -1/2 instead of -1/4, due to there being an extra x2
The link to the answer is here:https://imgur.com/gallery/UJIcLIW
Can someone explain why there is an extra x2???

Because they have applied the chain rule twice and I suspect you have not.
Original post by zetamcfc
Because they have applied the chain rule twice and I suspect you have not.

I did apply the chain rule, as far as I know.
Original post by PeaceMinusOne
I did apply the chain rule, as far as I know.

For the derivative of cot(2x)?
Original post by PeaceMinusOne
I did apply the chain rule, as far as I know.

You will need to apply it twice, not once.
Original post by zetamcfc
For the derivative of cot(2x)?

I did it for (cot(2x))^2

and I got, -2cosec^2(2x)cot(2x)
Original post by flumefan1
You will need to apply it twice, not once.

Do you know why it needs to be applied twice?
I think it has something to do with the 2x, maybe the double angle formula is involved some way?
Original post by PeaceMinusOne
Do you know why it needs to be applied twice?

I would be able to explain better if I knew the original question, but to find the derivative of some functions you'll need to do it twice.
Did you get my PM?
Original post by PeaceMinusOne
Do you know why it needs to be applied twice?

By definition? You need to revisit the chain rule.
Original post by flumefan1
I would be able to explain better if I knew the original question, but to find the derivative of some functions you'll need to do it twice.

The question is 2b and I have also attached my working out.
(edited 3 years ago)
What would you get for differentiating
cot^2(u)
(edited 3 years ago)
Original post by mqb2766
What would you get for differentiating
cot^2(x)

the answer is -2cosec^2(x)cot(x) I believe..
Original post by PeaceMinusOne
the answer is -2cosec^2(x)cot(x) I believe..

Yes. Now let
x = 2z
What's the derivative with respect to z?
Original post by PeaceMinusOne
The question is 2b and I have also attached my working out.

Use substitution, where u = cot(2x), so u(1)(x) (first derivative) = -2cosec2(2x), and dx = -1/2*sin2(2x).
Substituting this in gives the integral of -0.5u, which is -u2/4.
Undoing the substitution gives -1/4* cot2(2x) + C as required.
Original post by mqb2766
Yes. Now let
x = 2z
What's the derivative with respect to z?

the derivative of x=2z with respect to z is just 2?
Original post by flumefan1
Use substitution, where u = cot(2x), so u(1)(x) (first derivative) = -2cosec2(2x), and dx = -1/2*sin2(2x).
Substituting this in gives the integral of -0.5u, which is -u2/4.
Undoing the substitution gives -1/4* cot2(2x) + C as required.

A point on that, why does wolfram give a different answer? https://www.wolframalpha.com/input/?i=integral+%28cosec+%282x%29%29%5E2+cot%282x%29
Reply 18
Original post by PeaceMinusOne
the derivative of x=2z with respect to z is just 2?


So you bring that derivative out to the front, where there's already a factor of 2...
Original post by zetamcfc
A point on that, why does wolfram give a different answer? https://www.wolframalpha.com/input/?i=integral+%28cosec+%282x%29%29%5E2+cot%282x%29

It doesn't?

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