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

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

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

amistre64
 2 years ago
Best 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

mags093
 2 years ago
Best ResponseYou've already chosen the best response.0thats what it looks like properly :)

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

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.2so lets start by taking the derivative of that

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2yeah, just put u= 1/x du=... ?

Spacelimbus
 2 years ago
Best ResponseYou've already chosen the best response.0exactly, @hartnn, this substution does the trick.

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

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

mags093
 2 years ago
Best ResponseYou've already chosen the best response.0the integral exists anyway! i know that much

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

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

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

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

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.2let u= 1/x du/dx = 1/2x^2 du = 1/2x^2 dx

mags093
 2 years ago
Best ResponseYou've already chosen the best response.0how do i get the derivative of 1/x?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.21/x = x^1 which is then just the power rule .... which means i got a bad 2 in there :)

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.2im thinking of a sqrt function ..... silly me

mags093
 2 years ago
Best ResponseYou've already chosen the best response.0what do you mean a bad 2? :)

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.2x^1 goes to x^(2) 1/x goes to 1/x^2 NOT 1/2x^2

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.2so just pull out the 1/6 and integrate the easy way

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

mags093
 2 years ago
Best ResponseYou've already chosen the best response.0oh yes i see :) got confused for a minute!

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

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.2you got it from here?

mags093
 2 years ago
Best ResponseYou've already chosen the best response.0\[\frac{ e^\frac{ 1 }{ x } }{ 6 }\]

mags093
 2 years ago
Best ResponseYou've already chosen the best response.0something like that right?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.2yes, but apply your limits

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

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

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

mags093
 2 years ago
Best ResponseYou've already chosen the best response.0so i put 1 and 2 in for x?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.23 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

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

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

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

mags093
 2 years ago
Best ResponseYou've already chosen the best response.0if i work that out it gives me something like 0.782?

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

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

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