A community for students.
Here's the question you clicked on:
 0 viewing
mags093
 3 years ago
please help?
Evaluate the definite integral (if it exists)
intergral (e^1/3)/6x^2 dx from 1 to 2 ?
mags093
 3 years ago
please help? Evaluate the definite integral (if it exists) intergral (e^1/3)/6x^2 dx from 1 to 2 ?

This Question is Closed

amistre64
 3 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
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0thats what it looks like properly :)

amistre64
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.2so lets start by taking the derivative of that

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

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

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

amistre64
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0the integral exists anyway! i know that much

amistre64
 3 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
 3 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
 3 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
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0how do i get the derivative of 1/x?

amistre64
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.2im thinking of a sqrt function ..... silly me

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

amistre64
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.2so just pull out the 1/6 and integrate the easy way

amistre64
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0oh yes i see :) got confused for a minute!

amistre64
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.2you got it from here?

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

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

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

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

hartnn
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0so i put 1 and 2 in for x?

amistre64
 3 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
 3 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
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0if i work that out it gives me something like 0.782?

mags093
 3 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
 3 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
 3 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 :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.