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# Integration Problem 2 Watch

1. I have been set the following question
.
How do I go about factorising the as it doesn't seem to factorise.

Barney
2. (Original post by Barney63)
I have been set the following question
.
How do I go about factorising the as it doesn't seem to factorise.

Barney
Start off by completing the square.
3. HINT:
4. Depending on the exam board, after completing the square, you may be able to use some standard formulae given in the formula book which makes this question fairly easy. If not then the question is much longer.
5. Right I have done this question, but get a different answer to Wolfram Alpha.
I am the same as WA up until
What I have done is let
that giving me subbing s and u back in
WA on the other hand does let and giving subbing s and u back in
Why?

Barney
6. (Original post by Barney63)
Right I have done this question, but get a different answer to Wolfram Alpha.
I am the same as WA up until
What I have done is let
that giving me subbing s and u back in
WA on the other hand does let and giving subbing s and u back in
Why?

Barney
why have you let s=u/4? that doesn't help you because then s^2 = u^2/16!
And you can't integrate a function of s with respect to u - you have to convert the whole integral consistently.
7. Sorry I didn't follow that.

Barney
8. (Original post by Barney63)

Barney
You are making this much too hard. Why have you taken the factor of out? This has created an unnecessary fractional denominator.
9. then let u=x+1
then
then

Or how would you recommend doing it?

Barney
10. No substitution is necessary but, if you feel the need to make one, stop here and look at the standard integrals in your formula book.

(Original post by Barney63)

then let

11. We haven't been given/use a formula book

Barney
12. (Original post by Barney63)
Right I have done this question, but get a different answer to Wolfram Alpha.
I am the same as WA up until
What I have done is let
You should to substitute
that giving me
1. Your substitution here is wrong totally
AS you wrote let s be . OK.
then

and you have to substitute the du factor too.
Without this, the integral in that form you wrote gives different funtion. Namely

because s is a constant with respect to u. (integration factor is du here)
THe right method would be:
u=4s ->ratio of differentials ->du=4ds

and now use the t=2s substitution
from this

and

which is a base integral for t.
2. With you will get similar form more simple way
then

3. Most simple method without substitution is to use the known rules for
differentiation, composite function and the chain rule.

13. (Original post by Barney63)
We haven't been given/use a formula book

Barney
What course are you studying?
14. Its the Institute of Maths Polymaths course, an access course for the maths degree.

Barney
15. (Original post by Barney63)
Its the Institute of Maths Polymaths course, an access course for the maths degree.

Barney
Ok now I understand why you appeared to be making a meal of this.

A Level students are provided with a booklet containing this standard integral (along with many others):

16. So that would give

Barney
17. (Original post by Barney63)
So that would give

Barney
Yes (if you remember the du at the end of your integral).

You might like to think about how you could prove this standard result (it isn't as difficult as you might think as you know the answer you are seeking).
18. (Original post by Mr M)
Ok now I understand why you appeared to be making a meal of this.

A Level students are provided with a booklet containing this standard integral (along with many others):

I have never seen anything like that in my life...
19. Thanks for the help, you have made things much clearer.
Looking back in my notes we were given that formula in class.
Once again thank you.

Barney
20. (Original post by Barney63)
Thanks for the help, you have made things much clearer.
Looking back in my notes we were given that formula in class.
Once again thank you.

Barney
Ok ... you are welcome.

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