Register to reply

How the heck do I integrate sin(1/x) ?

by Matt Jacques
Tags: heck, integrate, sin1 or x
Share this thread:
Matt Jacques
#1
Feb18-04, 06:06 PM
P: 80
I tried parts by integration but Im caught in an endless loop of ever growing in complexity integrals! I must be missing something.
Phys.Org News Partner Science news on Phys.org
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history
matt grime
#2
Feb18-04, 06:21 PM
Sci Advisor
HW Helper
P: 9,396
is that an indefinite or definite integral?
HallsofIvy
#3
Feb18-04, 08:24 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,353
Do you have any reason to believe its anti-derivative is an elementary function?

PrudensOptimus
#4
Feb18-04, 11:46 PM
P: 640
How the heck do I integrate sin(1/x) ?

easy man

here's the answer:


-cosintegral[1/x] + xSin[1/x]
Matt Jacques
#5
Feb19-04, 06:47 AM
P: 80
I got that, too. No way to further simplify?
matt grime
#6
Feb19-04, 07:21 AM
Sci Advisor
HW Helper
P: 9,396
apart from that the integral of 1/x is log(x) you mean?
NateTG
#7
Feb19-04, 10:02 AM
Sci Advisor
HW Helper
P: 2,538
If you're desperate, you could try working out a Taylor/Mclaurin series for it, and seeing if the integral of that is recognizable.
Spectre5
#8
Feb20-04, 04:12 PM
P: 186
You can use a Maclaurin series to evaluate (or at least approximate) it...knowing that

[tex]sin(x)=\sum_{n=0}^{\infty}\frac{(-1)^nx^{(2n+1)}}{(2n+1)!}[/tex]


you can replace x with 1/x and integrate to get:


[tex]\int sin(\frac{1}{x})=\sum_{n=0}^{\infty}\frac{(-1)^{n-1}}{2(2n+1)!x^{2n}}[/tex]
PrudensOptimus
#9
Feb20-04, 07:10 PM
P: 640
Originally posted by matt grime
apart from that the integral of 1/x is log(x) you mean?

Wrong. ∫1/x dx = ln |x| + C.

∫1/(x(ln 10)) dx = log |x| + C.
master_coda
#10
Feb20-04, 07:13 PM
P: 678
Originally posted by PrudensOptimus
Wrong. ∫1/x dx = ln |x| + C.

∫1/(x(ln 10)) dx = log |x| + C.
When a mathematician says "log" they are generally talking about the natural logarithm.
NateTG
#11
Feb20-04, 08:32 PM
Sci Advisor
HW Helper
P: 2,538
Originally posted by master_coda
When a mathematician says "log" they are generally talking about the natural logarithm.
Right, and the rest of the time they usually mean [tex]log_2[/tex]
but anything other than [tex]log_e[/tex] gets a base.
master_coda
#12
Feb20-04, 11:56 PM
P: 678
Originally posted by NateTG
Right, and the rest of the time they usually mean [tex]log_2[/tex]
but anything other than [tex]log_e[/tex] gets a base.
I don't see too many mathematicians refer to [itex]\log_2[/itex] as [itex]\log[/itex].
NateTG
#13
Feb21-04, 12:22 AM
Sci Advisor
HW Helper
P: 2,538
It's typically for math/cs tpe situations and usually only applies to situations where hte base is not particuarly important.
matt grime
#14
Feb21-04, 03:12 AM
Sci Advisor
HW Helper
P: 9,396
Originally posted by PrudensOptimus
Wrong. ∫1/x dx = ln |x| + C.

∫1/(x(ln 10)) dx = log |x| + C.

yes, i did omit the modulus sign, however you should probably be told that log always means base e. This is completely standard in mathematics, and just one more thing they misteach at high school


After all what other base would you possibly want?
curiousbystander
#15
Feb24-04, 11:12 AM
P: 20
This might help too:

sin(1/x) is an odd function (meaning f(-x) = -f(x)).

The definite integral of any odd function on the interval [-a,a] is 0.
matt grime
#16
Feb24-04, 12:04 PM
Sci Advisor
HW Helper
P: 9,396
one generally wouldn't integrate over a region where the function is not defined. (no choice at zero can make it continuous, interestingly enough, not that that's either here or there, and not that any choice would make the integral be anything but zero anyway, though 0 is the only choice that keeps it a genuine odd function.)
curiousbystander
#17
Feb24-04, 05:17 PM
P: 20
I should have been more careful when answering, but isn't the integral still well defined since {0} is a set of measure 0?
NateTG
#18
Feb24-04, 05:28 PM
Sci Advisor
HW Helper
P: 2,538
Do you mean to use Lebesgue integration?

[tex]\lim_{x \rightarrow 0}[/tex] might also not exist and thus cause problems.


Register to reply

Related Discussions
What the heck? Precalculus Mathematics Homework 3
What the heck is this?! Current Events 8
What the heck? General Discussion 1
What the heck General Math 5
What the heck? Forum Feedback & Announcements 6