anonymous
  • anonymous
what is integral of (cos x) / x ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
What integration techniques do you have right now?
anonymous
  • anonymous
techniques? like?
anonymous
  • anonymous
u-substitution parts trig substitution etc.

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anonymous
  • anonymous
i just wanna find out derivative of cosx/x between 3 pi/2 and pi/2
anonymous
  • anonymous
and then the integral of cos x/x
anonymous
  • anonymous
The derivative would be the slope of the tangent line, the integral is the area of the region. Two different (yet related) things.
anonymous
  • anonymous
i have tried finding out integral of cos x/x but it was an infinite loop!!! need an answer for this plz
anonymous
  • anonymous
i have tried finding out integral of cos x/x but it was an infinite loop!!! need an answer for this plz
anonymous
  • anonymous
ntegration by parts is a heuristic rather than a purely mechanical process for solving integrals; given a single function to integrate, the typical strategy is to carefully separate it into a product of two functions ƒ(x)g(x) such that the integral produced by the integration by parts formula is easier to evaluate than the original one.
anonymous
  • anonymous
So it sounds like you tried parts. Which is what I would do. The integral ends up being: \[[\ln(x)\cos(x)+\sin(x)/x]/2 + c\]
anonymous
  • anonymous
uh huh.
anonymous
  • anonymous
how did u get that answer? can u plz explain the steps..
anonymous
  • anonymous
I set u = cos(x) and dv = dx/x and solved for du and v. Then I put in uv - ∫v du and had to use parts again using u = sin(x) and dv = ln(x)dx and solved for du and v again. This time I ended up with ln(x)cos(x)+sin(x)/x - ∫cos(x)/x dx = ∫cos(x)/x dx (the original problem) then I added ∫cos(x)/x dx to both sides and divide by two.
anonymous
  • anonymous
hmm..so derv of cos x =-sinx and intg(dv) =1/x dx right?
anonymous
  • anonymous
du = -sin(x)dx and v = ln(x) for the first parts.
anonymous
  • anonymous
the formula is , u int (v)- int{d/dx(u) . int(v)}dx right?
anonymous
  • anonymous
∫u dv = u*v - ∫v du is what integration by parts states.
anonymous
  • anonymous
intr(u) dv or integral (uv)?
anonymous
  • anonymous
dont we ve any formula as "something / somethig" in intergral as we ve for derivatives?
anonymous
  • anonymous
This integral cannot be represented in terms of transcendental and algebraic functions. You can only represent it with series.
anonymous
  • anonymous
if we have lower limit as pi/2 and upper one as 3 pi/2 then?
anonymous
  • anonymous
as the sin terms become all zeroes with pi/2 's
anonymous
  • anonymous
It can't be done with any method other than series, even if you constrained the limits.
anonymous
  • anonymous
im sry the cos terms
anonymous
  • anonymous
ohh..isnt there any other way out?
anonymous
  • anonymous
Not from what I researched online. You may be able to use power series. However, u-substitution, backwards u-substitution, integration by parts, partial fractions, etc. will not solve this integral. If I could remember power series from three years ago I could help, but I don't remember :(
anonymous
  • anonymous
ohh :(...anyways thanks
anonymous
  • anonymous
gotta findout frm somewhere else then
anonymous
  • anonymous
thanks Tbates and jshowa
anonymous
  • anonymous
hey can u just temme how do i join the group chat here??
anonymous
  • anonymous
i have got lot many questions to ask....!!!
anonymous
  • anonymous
anybody there?????
anonymous
  • anonymous
I'm not sure what you do, I tried typing something and it didn't work for me. You can just ask another question.
anonymous
  • anonymous
hmm...
anonymous
  • anonymous
so in such a case we get loops isnt it?
anonymous
  • anonymous
even if got the upper n lower limits for that
anonymous
  • anonymous
can anyone answer this?
anonymous
  • anonymous
I'm not sure, however, I intend on answering this question once I refresh myself with series. So, check back in a day or so. The limits really don't matter because you still have to evaluate the integral before you use them. And with integration by parts, you will continually get integrals that must be done with parts and it will never end. You must either construct a power series or Taylor series of cosx/x and estimate the integral.
anonymous
  • anonymous
yeah..that actually does go on n on..
anonymous
  • anonymous
n theres one more thing
anonymous
  • anonymous
n theres one more thing
anonymous
  • anonymous
tangent is a plane and normal is a line on that plane..is this staement correct?
anonymous
  • anonymous
anyone there?
anonymous
  • anonymous
integration by parts would do it
anonymous
  • anonymous
make 1/x your dv and and your u cos(x)
anonymous
  • anonymous
hmm...and how wud the final answer look like?

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