Integrate $$\cos(x^2)$$ and $$\sin(x^2)$$

Question

amistre64 · Answer

shuld prolly use a series equivalent

amistre64 · Answer

there are no elementary functions whose derivatives are as such

anonymous · Answer

Which series would you recommend here (I've never integrated by converting to a series before)?

amistre64 · Answer

the taylor series for sin or cos turns the trig into a polynomial; and polys are easy to integrate

amistre64 · Answer

cos is an even function, so we that uses the even parts .... if i recall it correctly
$$cos(u)=\sum\frac{x^{2n}}{(2n)!}$$maybe??

amistre64 · Answer

forgot an alternating +-+- , but the rest might be ok :)

anonymous · Answer

http://furius.ca/cqfpub/doc/series/series.pdf cheat sheet for maclaurin series, sorry to sneak in here, but it maybe helps - I have to be leaving now, enjoy (-:

amistre64 · Answer

cheat sheets are good, as long as you understand the mechanics behind it imo

anonymous · Answer

In general, is there any easy way to condense a Taylor series back into a nice function (obviously not here as you said)?

amistre64 · Answer

since a taylor is an infinite series, prolly not; but thats the hand we are dealt with these types of functions

anonymous · Answer

Thanks!

amistre64 · Answer

youre welcome, and good luck