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mags093
Group Title
please help?
Evaluate the definite integral (if it exists)
intergral (e^1/3)/6x^2 dx from 1 to 2 ?
 one year ago
 one year ago
mags093 Group Title
please help? Evaluate the definite integral (if it exists) intergral (e^1/3)/6x^2 dx from 1 to 2 ?
 one year ago
 one year ago

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amistre64 Group TitleBest ResponseYou've already chosen the best response.2
e^1/3 looks like a variable, but its not; its just a constant
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
\[\int\limits\limits_{1}^{2} \frac{ e^\frac{ 1 }{ x } }{ 6x^2 } dx\]
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
\[\huge \int\limits\limits_{1}^{2} \frac{ e^\frac{ 1 }{ x } }{ 6x^2 } dx\] is that 1/3 or 1/x? need to verify
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
thats what it looks like properly :)
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{ 1 }{ x }\]
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
well, if this is going to be simple than with any luck it will come from something like:\[\Large \frac d{dx}e^{1/x}\]
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
so lets start by taking the derivative of that
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
yeah, just put u= 1/x du=... ?
 one year ago

Spacelimbus Group TitleBest ResponseYou've already chosen the best response.0
exactly, @hartnn, this substution does the trick.
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
do we not have to do something with the derivavtive of 6x^2?
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
we should verify that if its going to be simple first and see if we can modifiy it with a useful form of "1"
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
the integral exists anyway! i know that much
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
\[\frac d{dx}e^{1/x}=\frac{e^{1/x}}{2x^2}\]agree?
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
where did the 2x^2 come from? is the derivative of 6x^2 not 12x?
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
your confusing your rules .... its best to see these things on a more holistic level :)
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
\[\frac d{dx}e^{u(x)}=\frac{d}{dx}u(x)~e^{u(x)}=u' ~e^u\]
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
let u= 1/x du/dx = 1/2x^2 du = 1/2x^2 dx
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
how do i get the derivative of 1/x?
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
1/x = x^1 which is then just the power rule .... which means i got a bad 2 in there :)
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
im thinking of a sqrt function ..... silly me
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
what do you mean a bad 2? :)
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
x^1 goes to x^(2) 1/x goes to 1/x^2 NOT 1/2x^2
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
oh ok i get ya now
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
so just pull out the 1/6 and integrate the easy way
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
wheres the 1/6?
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
\[\int\frac{e^{1/x}}{6x^2}dx\] \[\int\frac16 \frac{e^{1/x}}{x^2}dx\] \[\frac16\int \frac{e^{1/x}}{x^2}dx\]
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
oh yes i see :) got confused for a minute!
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
just becasue you were doing vector calculus the other day doesnt mean you have to forget the fundamentals ;)
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
you got it from here?
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{ e^\frac{ 1 }{ x } }{ 6 }\]
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
something like that right?
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
yes, but apply your limits
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
what do you mean?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
not, e^(1/x) /6
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
i mean ....\[\int_{a}^{b}f(x)~dx=F(b)F(a)\]
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
plus you need to change limits beforehand, u=1/x when x=1,u=1 when x=2, u=1/2
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
but u=1/x?
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
if you do a usub, then you need to do hartnns route otherwise its just e^(1/x)/6 applied at 1 and 2
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
so i put 1 and 2 in for x?
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
3 methods that im aware of; complete usub changes limits to us partial usub where you undo the u back to x and just working thru a normal integration were nothing is changed about.... which is what i did
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{ e^u }{ 6 }\]
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
\[\int_{1}^2f(x)dx=F(2)F(1)\] and we determined that \[F(x)=\frac16e^{1/x}\]
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
and then i got that^
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
so i sub in 2 and 1 for x then subtract them? is that it?
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
yes\[\frac16(e^{1/2}e^{1/1})\] yes\[\frac16(e^{1/2}e)\]
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
if i work that out it gives me something like 0.782?
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
if i just leave it as \[\frac{ 1 }{ 6 } (e^\frac{ 1 }{ 2 }  e\]
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
did u mean 0.1782 ? and you can keep your answer as 1/6(e^(1/2)e)
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
when i worked it out it was 0.782 but if i leave it as the 1/6... it works out just the same :)
 one year ago

mags093 Group TitleBest ResponseYou've already chosen the best response.0
thanks for the help :)
 one year ago
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