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shahzadjalbani
 3 years ago
integrate sin (x^2) form 0 to pi
shahzadjalbani
 3 years ago
integrate sin (x^2) form 0 to pi

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shahzadjalbani
 3 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{\pi} \sin x ^{2} dx\]

eliassaab
 3 years ago
Best ResponseYou've already chosen the best response.1You cannot do that in closed from.

eliassaab
 3 years ago
Best ResponseYou've already chosen the best response.1You can do it numerically.

ProgramGuru
 3 years ago
Best ResponseYou've already chosen the best response.0first 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

sami21
 3 years ago
Best ResponseYou've already chosen the best response.2the best option is to go for numerical integration f(x)=sin(x^2) using simpson's rule with n=4 h=(pi0)/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

ProgramGuru
 3 years ago
Best ResponseYou've already chosen the best response.0@sami21 Can you please explain to me what is simpson's rule?

cherylim23
 3 years ago
Best ResponseYou've already chosen the best response.0Sami21, just wondering, why does other sources suggest that the answer is 0.77265 instead?

sami21
 3 years ago
Best ResponseYou've already chosen the best response.2yeah 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=(ba)/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

ProgramGuru
 3 years ago
Best ResponseYou've already chosen the best response.0@sami21 Big thanks man!!

sami21
 3 years ago
Best ResponseYou've already chosen the best response.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

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.0here is a very nice integral and possible to solve analytically ; if u r interested \[\large \int\limits_{0}^{\infty} \sin x^2 \ dx\]

sami21
 3 years ago
Best ResponseYou've already chosen the best response.2yes i can do this !!!!!!

sami21
 3 years ago
Best ResponseYou've already chosen the best response.2taylor series about a=0 for sin(x) is \[sin(x)=xx^3/3!+x^5/5!x^7/7!+...\] replace x by x^2 i the above \[sin(x^2)=x^2x^6/3!+x^{10}/5!x^{14}/7!+...\] now you can integrate both sides and you will get the result because you will have just to integrate polynomial

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.0yes thats right it will give a series for u but not the exact answer here is my solution ; It worths watching! :)

sami21
 3 years ago
Best ResponseYou've already chosen the best response.2yup i got this in BS grewall Highier Engineering Mathematics thanks i think fourier integral also works here

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.0yes fourier will work also....
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