Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

shahzadjalbani

  • 3 years ago

integrate sin (x^2) form 0 to pi

  • This Question is Closed
  1. shahzadjalbani
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  2. hba
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    akbar jatoi jalbani

  3. eliassaab
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You cannot do that in closed from.

  4. eliassaab
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You can do it numerically.

  5. ProgramGuru
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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

  6. sami-21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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

  7. ProgramGuru
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @sami-21 Can you please explain to me what is simpson's rule?

  8. cherylim23
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Sami-21, just wondering, why does other sources suggest that the answer is 0.77265 instead?

  9. sami-21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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

  10. ProgramGuru
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @sami-21 Big thanks man!!

  11. sami-21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @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

  12. mukushla
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  13. sami-21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes i can do this !!!!!!

  14. sami-21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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

  15. mukushla
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes thats right it will give a series for u but not the exact answer here is my solution ; It worths watching! :)

    1 Attachment
  16. sami-21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yup i got this in BS grewall Highier Engineering Mathematics thanks i think fourier integral also works here

  17. mukushla
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes fourier will work also....

  18. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.