intergration Watch

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sarah12345
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#1
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how do i intergrate things like k/x ? is it something to do with logs? i cant find this in c1 or c2 but i need to do it can neone help?
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lgs98jonee
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(Original post by sarah12345)
how do i intergrate things like k/x ? is it something to do with logs? i cant find this in c1 or c2 but i need to do it can neone help?
k/x=k multpilied by x^-1

x^-1 when integrated goes to lnx

so you get klnx
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Fermat
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The integral of 1/x is ln(x). (a standard result)

If you have 1/x multiplied by a constant. i.e. k/x, then just multiply the standard result (1/x) by the same constant.

So if you have k/x then the integral is k.ln(x).
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J.F.N
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Its just k.ln(x)
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Gauss
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(Original post by sarah12345)
how do i intergrate things like k/x ? is it something to do with logs? i cant find this in c1 or c2 but i need to do it can neone help?
Rewrite it as k(x^-n) and use the formula y' = ax^n, y = [a/(n+1)]x^(n+1). Only use this formula if n =/= -1.

In the case when n=-1, use the fact that y' = kx^(-1), y = klogx.

Euclid.
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evariste
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dont forget the constant of integration though.
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Gauss
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(Original post by evariste)
dont forget the constant of integration though.
Oh them, they're evil. Always catch me out

Euclid.
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evariste
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(Original post by Euclid)
Oh them, they're evil. Always catch me out

Euclid.
especially for ln. teachers start calling c things like ln c! confusion all round.
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sarah12345
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thanks for the help!

im trying to do this question

X has a probability density function

f(x)= k/x 1<= x <= 2
0 otherwise


i found that k was 1/ln 2

but now im stuck on finding the expectation and keep getting the wrong answer can anyone help? thanks

also if i know ln x = y how can i work out what x is?
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kikzen
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E(X) = sum(1 to 2) x*f(x)
=1(1/ln2) + 2(1/2ln2)
=2/ln2

?
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kikzen
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#11
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ln x = y
e^(ln x) = e^y
x = e^y
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sarah12345
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(Original post by kikzen)
ln x = y
e^(ln x) = e^y
x = e^y
thankyou!
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sarah12345
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(Original post by kikzen)
E(X) = sum(1 to 2) x*f(x)
=1(1/ln2) + 2(1/2ln2)
=2/ln2

?
the answer given is 1/ln 2 ?????????????????
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davros
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If the distribution is continuous (not discrete) then you need to integrate x * f(x) between the limits (not sum it).

Then you should get 1/ln 2.

Davros
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kikzen
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guuhhh i hate stats
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[email protected]
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(Original post by kikzen)
guuhhh i hate stats
dont we all
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sarah12345
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#17
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(Original post by davros)
If the distribution is continuous (not discrete) then you need to integrate x * f(x) between the limits (not sum it).

Then you should get 1/ln 2.

Davros
so is this right?

i intergrate between 1 and 2 x* k/x which would just give me k?
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davros
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#18
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Yes, and you have already worked out what k is...
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sarah12345
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#19
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(Original post by davros)
Yes, and you have already worked out what k is...
thankyou for all the help!
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