How can I integrate \sin{x^2} using Taylor series?

[euler_fan]

I would appreciate a hint as how to integrate the following, after some thought, I used Taylor series and integrated in term.

Thanks

$$\int\sin{x^2}$$

 

[cristo]

Use the identity $\sin^2x=\frac{1}{2}(1-\cos(2x))$. This is derived from the double angle formula for cosine; $\cos(2x)=\cos^2x-\sin^2x=1-2\sin^2x$. Rearranging gives the result.

 

[mathwonk]

sin(x^2) apparently has no elementary integral. hence a taylor series is about all you can do. a discussion of such questions is in a paper on brian conrad's page at umichigan.

sin^2(x) of course does have, as can be seen by using integration by parts, or the trig identity suggested above.

 

[cristo]

Sorry... I misread it as sin^2(x)!

 

[Gib Z]

... after some thought, I used Taylor series and integrated in term.

Good Work, Thats the best you can do.