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# Lots of maths help needed watch

1. Basically I don't understand anything. Any help would be so much appreciated or I'm going to fail...

The one thats bugging me the most right now...Integration by parts of

I have tried it by making

and solving as a normal partial fraction to get A = =2 and B = 2 but these numbers don't seem to work and I don't know where I've gone wrong...
2. (Original post by fn_101)
Basically I don't understand anything. Any help would be so much appreciated or I'm going to fail...

The one thats bugging me the most right now...Integration by parts of

I have tried it by making

and solving as a normal partial fraction to get A = =2 and B = 2 but these numbers don't seem to work and I don't know where I've gone wrong...
Your partial fractions are split wrong. When there is a repeated factor in the denominator you need to include it from power 1 all the way up to the power it is in the expression.

I.e. in this case you need to use
3. (Original post by ukdragon37)
Your partial fractions are split wrong. When there is a repeated factor in the denominator you need to include it from power 1 all the way up to the power it is in the expression.

I.e. in this case you need to use

Okay, so I tried it and got as far as following through this to get c=1 but i don't know what to put as the values of x to find A or B because they both have an x-2 ....
4. (Original post by fn_101)
Basically I don't understand anything. Any help would be so much appreciated or I'm going to fail...

The one thats bugging me the most right now...Integration by parts of

I have tried it by making

and solving as a normal partial fraction to get A = =2 and B = 2 but these numbers don't seem to work and I don't know where I've gone wrong...
your factorising of the denominator is wrong. its a cubic function, so you've got to have 3 partial fractions
5. (Original post by fn_101)
Okay, so I tried it and got as far as following through this to get c=1 but i don't know what to put as the values of x to find A or B because they both have an x-2 ....
You need to expand out and compare the coefficients of constants, x, and x^2 etc. on left and right to get values for A and B.

EDIT: Also check the c value you've already got.
6. (Original post by ukdragon37)
You need to expand out and compare the coefficients of constants, x, and x^2 etc. on left and right to get values for A and B.

EDIT: Also check the c value you've already got.
Okay I have A= -2, B = -2 and C = 2....does that sound better to continue with?
7. (Original post by fn_101)
Okay I have A= -2, B = -2 and C = 2....does that sound better to continue with?
Yes.
8. (Original post by ukdragon37)
Yes.
Okay, right so using them it seems easier to intergrate but how do you intergrate

? I have used ln for the other functions (A and C) to get -2 ln x and 2 ln (x+2)
9. (Original post by fn_101)
Okay, right so using them it seems easier to intergrate but how do you intergrate

? I have used ln for the other functions (A and C) to get -2 ln x and 2 ln (x+2)
Surely that is easier to integrate than A and C? If you are doing this question then you should have done how to integrate already.
10. I am also really stuck on these integrations..

using integration by substitution

and

if

Use inegration by parts to find the integral of

11. (Original post by fn_101)
I am also really stuck on these integrations..

using integration by substitution
We generally can deal with cosx, but cos(rootx) is harder. So the first substitution worth trying is u = sqrt(x)

if

Use inegration by parts to find the integral of

Let u = arctanx and dv/dx = x simply because the question hints at the differentiaton of arctanx. Although, in general, it's a good idea to let u = x (or whatever polynomial term).
12. (Original post by fn_101)
Basically I don't understand anything. Any help would be so much appreciated or I'm going to fail...

The one thats bugging me the most right now...Integration by parts of

I have tried it by making

and solving as a normal partial fraction to get A = =2 and B = 2 but these numbers don't seem to work and I don't know where I've gone wrong...

http://www.wolframalpha.com/input/?i=integrate+(-2/x^2)

wolframalpha was my saviour for a-level

you can put in a problem and it solves it, even giving steps for the working.

13. (Original post by Swayum)
We generally can deal with cosx, but cos(rootx) is harder. So the first substitution worth trying is u = sqrt(x)

Let u = arctanx and dv/dx = x simply because the question hints at the differentiaton of arctanx. Although, in general, it's a good idea to let u = x (or whatever polynomial term).
For the first one I tried...

Then replaced the denominator and the dx, and took the 2 outside (or is it supposed to be 1/2 outside ? )

Then ended up with the integral of 2 cos u which I can integrate

For the second one I ended up with something I can't see myself integrating!

I dunno where I went wrong...
14. (Original post by fn_101)
For the second one I ended up with something I can't see myself integrating!

I dunno where I went wrong...
Multiply together the two fractions under the integral sign. Can you split up the fraction into a number and a fractional remainder?
15. (Original post by ukdragon37)
Multiply together the two fractions under the integral sign. Can you split up the fraction into a number and a fractional remainder?
You mean to get

I'm confused..
16. (Original post by fn_101)
You mean to get

I'm confused..
First note that

Now can you perform some sort of polynomial long division (or otherwise) on the fraction in the integral to split it into "a whole number" + "a fraction in terms of x"?
17. (Original post by ukdragon37)
First note that

Now can you perform some sort of polynomial long division (or otherwise) on the fraction in the integral to split it into "a whole number" + "a fraction in terms of x"?
Yes, I can Ahh thankyou!
18. Sorry to be a pain everyone but I do not understand limits at all.... for example, use the limit definition to show

then
19. (Original post by fn_101)
Sorry to be a pain everyone but I do not understand limits at all.... for example, use the limit definition to show

then
What level of maths are you at? What is your definition of a limit?

And don't worry, you're not being a pain or anything. Keep em coming.
20. (Original post by fn_101)
Sorry to be a pain everyone but I do not understand limits at all.... for example, use the limit definition to show

then
I suspect by "limit definition" you mean:

The thing to remember is that you can only substitute h with 0 once it is not in the denominator. Since the question gives you a value of x, why don't you put that in and see what happens?

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