Question

integrate sin (x^2) form 0 to pi

Answer 1

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

Answer 2

akbar jatoi jalbani

Answer 3

You cannot do that in closed from.

Answer 4

You can do it numerically.

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

@sami-21 Big thanks man!!

Answer 11

@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

Answer 12

here is a very nice integral and possible to solve analytically ; if u r interested

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

Answer 13

yes i can do this !!!!!!

Answer 14

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

Answer 15

yes thats right it will give a series for u but not the exact answer

here is my solution ; It worths watching! :)

Answer 16

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

Answer 17

yes fourier will work also....