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# Integration

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1. Can anyone please tell me how to integrate

cos(a(t-b)^2) w.r.t t where a and b are constants
2. (Original post by haazu)
Can anyone please tell me how to integrate

cos(a(t-b)^2) w.r.t t where a and b are constants
Do you have the answer to this?

Even wolfram can't integrate it. http://www.wolframalpha.com/input/?i...%29%5E2%29+dx+
3. Are you sure you've got that formula right? That's a very difficult integral to do (I'm not even sure it's possible to do without a computer).

Edit: to the poster above me, It's possible to do using wolfram: manipulate the integral then use wolfram to integrate cos (x^2), which gives you a result in terms of the Fresnel Integral, or just put numbers in instead of a and b and wolfram stops being confused e.g. http://www.wolframalpha.com/input/?i...8x-3%29%5E2%29

But yeah, I'm expecting a typo in the OP
4. I tried this on Maple and my laptop caught fire
5. Pic from mathcad attached, hope this helps.

You need to put the plus C in yourself, I know, useless isn't it

And unless I am missing something wolfram gives the same

int cos(a*(t-b)^2) w.r.t t = copy and paste and see.
Attached Thumbnails

6. A simple change of variables can reduce this to

which can't be expressed in terms of elementary functions. Do you have a range of integration? Did this integral arise in solving a different problem?
Attached Files
8. Integral.docx (13.4 KB, 38 views)
9. I can't seem to see that document - could you include a screenshot image?
10. (Original post by dantheman1261)
I can't seem to see that document - could you include a screenshot image?
11. I don't suppose the refers to by any chance?
12. yes unfortunately it does, j(or i) is sqrt(-1)

Any hope that this can be solved?
13. After trying a few things I can't see a way - the and are tricky to sort out if they're not equal (though someone else may be able to find a way, there might be a contour integral which can sort it out)

Might be best to try some numerical methods if you have the values of the constants?

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