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shahzadjalbani

integrate sin (x^2) form 0 to pi

  • one year ago
  • one year ago

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  1. shahzadjalbani
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    \[\int\limits_{0}^{\pi} \sin x ^{2} dx\]

    • one year ago
  2. hba
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    akbar jatoi jalbani

    • one year ago
  3. eliassaab
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    You cannot do that in closed from.

    • one year ago
  4. eliassaab
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    You can do it numerically.

    • one year ago
  5. ProgramGuru
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    first substitute x^2=z then 2xdx=dz putting x=sqrt(z) it will be dx=dz/(2sqrt(z)) changing limits and integrating by parts should give you the answer

    • one year ago
  6. sami-21
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    the best option is to go for numerical integration f(x)=sin(x^2) using simpson's rule with n=4 h=(pi-0)/4=pi/4 f(0)=sin(0)=0 f(pi/4)=sin(pi/4^2)=0.5784 f(pi/2)=sin(pi/2^2)=0.6242 f(3pi/4)=sin(3pi/4^2)=-0.668 f(pi)=sin(pi^2)=-0.4303 using sinpsons rule h/3(f(0)+4f(pi/4)+2f(pi/2)+4f(3pi/4)+f(pi)) put all the above values =0.12044

    • one year ago
  7. ProgramGuru
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    @sami-21 Can you please explain to me what is simpson's rule?

    • one year ago
  8. cherylim23
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    Sami-21, just wondering, why does other sources suggest that the answer is 0.77265 instead?

    • one year ago
  9. sami-21
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    yeah sure it is a technique for numerical integration the basic formula for this rule is as follows \[\int\limits_{a}^{b}f(x)=h/3(f0(x)+4f1(x)+2f2(x)+4f3(x)+2f4(x)+...fn(x))\] where h is the size of the interval and given by h=(b-a)/n where n is the no of subintervals (no of rectangles that gets added) just evaluate the function at the respective points the point with odd subscripts is multiplied by 4 and that with even subscripts is multiplied by 2 you can see this in the above formula you can visit the following also for detail http://en.wikipedia.org/wiki/Simpson's_rule

    • one year ago
  10. ProgramGuru
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    @sami-21 Big thanks man!!

    • one year ago
  11. sami-21
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    @cherylim23 yes correct answer is 0.77265 .it is a numerical technique there is always eror associated with numerical techniques we go for numerical technique when we do not have analytical solution ..the same answer can be achieved by simpson rule with n=20 or more you can go there at the following site and can compute the result with different size http://nastyaccident.com/calculators/calculus/simpsonsRule

    • one year ago
  12. mukushla
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    here is a very nice integral and possible to solve analytically ; if u r interested \[\large \int\limits_{0}^{\infty} \sin x^2 \ dx\]

    • one year ago
  13. sami-21
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    yes i can do this !!!!!!

    • one year ago
  14. sami-21
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    taylor series about a=0 for sin|(x) is \[sin(x)=x-x^3/3!+x^5/5!-x^7/7!+...\] replace x by x^2 i the above \[sin(x^2)=x^2-x^6/3!+x^{10}/5!-x^{14}/7!+...\] now you can integrate both sides and you will get the result because you will have just to integrate polynomial

    • one year ago
  15. mukushla
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    yes thats right it will give a series for u but not the exact answer here is my solution ; It worths watching! :)

    • one year ago
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  16. sami-21
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    yup i got this in BS grewall Highier Engineering Mathematics thanks i think fourier integral also works here

    • one year ago
  17. mukushla
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    yes fourier will work also....

    • one year ago
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