Question

what's the integral:

∫cos(x^2)

Answer 1

That's a pretty damn hard indefinite integral, IIRC. It's a Fresnel. And I don't how to solve it analytically. Check: http://mathworld.wolfram.com/FresnelIntegrals.html

Answer 2

use power series

Answer 3

Yeah, that's what I was going to post, :-). You can approximate it fairly easily to a power series, but to actually solve the integral analytically is near impossible, I think.

Answer 4

it is not 'near impossible' it is impossible in terms of elementary functions :)

Answer 5

yeah, these need middle school functions ;)

Answer 6

yes...those are much more powerful ;)

Answer 7

Maybe even some undergrad functions also :-). So, I think that the original problem reduces to approximate it to a power series and integrating it.

Answer 8

I get it from wolfram... how can I simplefied it?

Answer 9

Like I said, from Wolfram you will get the Fresnel anallytical solution. Remember that the Maclaurin series for cosx is:\[\cos(x) = \sum_{0}^{\infty}((-1)^{n}x^{2n})/2n!\] Just plug in x^2 for x and you will have the series for cos(x^2). Integrate it, and voila, you got your integral :-)

Answer 10

oops, from n = 0 to infinity. A typo there.

Answer 11

Thank you!!!!