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shahzadjalbani Group Title

integrate sin (x^2) form 0 to pi

  • 2 years ago
  • 2 years ago

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

    • 2 years ago
  2. hba Group Title
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    akbar jatoi jalbani

    • 2 years ago
  3. eliassaab Group Title
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    You cannot do that in closed from.

    • 2 years ago
  4. eliassaab Group Title
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    You can do it numerically.

    • 2 years ago
  5. ProgramGuru Group Title
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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

    • 2 years ago
  6. sami-21 Group Title
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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

    • 2 years ago
  7. ProgramGuru Group Title
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    @sami-21 Can you please explain to me what is simpson's rule?

    • 2 years ago
  8. cherylim23 Group Title
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    Sami-21, just wondering, why does other sources suggest that the answer is 0.77265 instead?

    • 2 years ago
  9. sami-21 Group Title
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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

    • 2 years ago
  10. ProgramGuru Group Title
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    @sami-21 Big thanks man!!

    • 2 years ago
  11. sami-21 Group Title
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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

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

    • 2 years ago
  13. sami-21 Group Title
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    yes i can do this !!!!!!

    • 2 years ago
  14. sami-21 Group Title
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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

    • 2 years ago
  15. mukushla Group Title
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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! :)

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

    • 2 years ago
  17. mukushla Group Title
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    yes fourier will work also....

    • 2 years ago
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