OCR C4 Intergration... Help! (Rep+)

Hey guys,

I am stuck on this and have been tearing my head apart!

The integral is (x+2)(2x-5)^5 dx.

Using x=(u-b)/a
x+2= (u-b)/a +2
2x-3= 2(u-b)/a -3

Now this is where I am stuck... (2x-3)^5= (2(u-b)/a -3)^5 ??

dx/du= -1/a

Now I have no idea what to do! The (2x-3)^5 I don't know how to simplifiy that.
And I don't know how to cancel down as the integral will be massive:/

Help guys!!

If anyone can use latex it would be great help to show it :smile:

Reply 1

cvqw1278

10

I feel for you. I HATE C4.

Reply 2

Susanne839

Latex - http://www.thestudentroom.co.uk/wiki/LaTeX

(edited 13 years ago)

Reply 3

J DOT A

OP

Original post by Susanne839

Latex - http://www.thestudentroom.co.uk/wiki/LaTeX

As for the integral - integration by parts?

Well it obv isn't as it gives you the substitution...

Reply 4

Farhan.Hanif93

18

Original post by J DOT A

Hey guys,

I am stuck on this and have been tearing my head apart!

The integral is (x+2)(2x-5)^5 dx.

Using x=(u-b)/a
x+2= (u-b)/a +2
2x-3= 2(u-b)/a -3

Now this is where I am stuck... (2x-3)^5= (2(u-b)/a -3)^5 ??

dx/du= -1/a

Now I have no idea what to do! The (2x-3)^5 I don't know how to simplifiy that.
And I don't know how to cancel down as the integral will be massive:/

Help guys!!

If anyone can use latex it would be great help to show it :smile:

I have no idea why you would try to generalise it in that way, it's much better to spot what is causing you problems in the integral and how to best deal with it via substitution. Regurgitating some formula for integration by substitution of that form from your reading of the textbook is not a good idea. Just let

u=2x-3

from the start and carry out the rest of the procedure.

(edited 13 years ago)

Reply 5

J DOT A

OP

Original post by Farhan.Hanif93

I have no idea why you would try to generalise it in that way, it's much better to spot what is causing you problems in the integral and how to best deal with it via substitution. Regurgitating some formula for integration by substitution of that form from your reading of the textbook is not a good idea. Just let

u=2x-5

from the start and carry out the rest of the procedure.

It says to use a substitution of the form ax+b=u, therefore using x=1/a(u-b)
Obv I wouldn't use this but it asks for it:/

Reply 6

Farhan.Hanif93

18

Original post by J DOT A

It says to use a substitution of the form ax+b=u, therefore using x=1/a(u-b)
Obv I wouldn't use this but it asks for it:/

When it asks you to use a substitution of that form, it wants you to identify the constants a and b. The easiest way to do this is by inspection. Like I said, if you can spot where the problem with integrating this lies, you will easily be able to tell what values for a and b will help.

If you can't spot it that way, look at what you've got. I think you can tell that the problem term is the (2x-3)^5. The problem with it is the fact that it's a composite function and you want to turn it to something which is just an ordinary function i.e. just a single polynomial term raised to the power of 5. What values of a and b will leave you with just (2x-3)^5=u^5?

Reply 7

Farhan.Hanif93

18

Original post by Susanne839

Latex - http://www.thestudentroom.co.uk/wiki/LaTeX

As for the integral - integration by parts?

Integration by parts should really be used as a last resort because in most cases there is a more simple way to do it.

Reply 8

Bjoorn

11

if you try the substitution u = 2x+5, you can manipulate it a bit and rewrite it as .5(u+9)=x+2. making these two substitution along with the one for dx should give you a very manageable integral

OCR C4 Intergration... Help! (Rep+)

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