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# Integration by substitution (P3) watch

1. Having trouble with Q11, exercise 4C, book P3:

Use u=x-1 to evaluate

Integral between 2 and 5 of x / [(x-1)^1/2]

Any help appreciated. I'm crap at these
2. du = dx

integral between 1 and 4 of (u+1)/(u^1/2) du

= integral between 1 and 4 of u^1/2 + u^-1/2 du

= [2/3 u^3/2 + 2 u^1/2] between 1 and 4

= 16/3 + 4 - 2/3 - 2

= 20/3
3. (Original post by elpaw)
= 20/3
Thanks

wow. 8 people voted. they all must be crazy
4. I voted "I'm crazy!". That's the only vote in fact. Look all you have to do for substitution is let something equal u and because you can't integrate f(u) with respect to x you want to put a du there instead of dx.

Well dx=(dx/du)(du) as the dus cancel out. In your case u=x-1 => x=u+1

Therefore:

(dx/du)=1

So (dx/du)(du)=du

You have to find int((x-1)^(1/2)).

So int(u^(1/2))

To work out your u limits:

u=x-1

Therefore:

When x=2 => u=1

When x=5 => u=4

So:

int(u^(1/2)) u=1..4

As elpaw said=(20/3)

Newton.
5. (Original post by Newton)
Well dx=(dx/du)(du) as the dus cancel out. In your case u=x-1 => x=u+1
Thats absolute crap, the du's DO NOT cancel. deyr not fractions, although they might behave as such.

Euclid
6. (Original post by Euclid)
Thats absolute crap, the du's DO NOT cancel. deyr not fractions, although they might behave as such.
Euclid
Until we can go to university and can study/prove why they behave like that we may as well pretend they cancel if it allows us to solve problems.
7. (Original post by Gaz031)
Until we can go to university and can study/prove why they behave like that we may as well pretend they cancel if it allows us to solve problems.
yeh of course, when i was doing a levels i was told the same thing. but newton said dey cancel out, which is nonesense. if it helps solving problems treat it as such, jus dont believe it or ull experience problems in ur future study (assuming ur doing maths at uni, if not then ignore that comment)
8. I think the trick is to remember when you can cancel them and when you can't. If you could get away with that all the time life would be easier
9. I like the fact that "i love integration" is a different option to "i'm crazy"
10. (Original post by Bekaboo)
I like the fact that "i love integration" is a different option to "i'm crazy"
yeah I was going to do 'I hate integration' and 'I'm crazy' but I got confused. If you vote at all then its pretty clear which option applies anyway

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