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Integration

Can anyone please tell me how to integrate

cos(a(t-b)^2) w.r.t t where a and b are constants
Reply 1
Avatar for raheem94
raheem94
13
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=integrate+cos%28a%28x-b%29%5E2%29+dx+
Reply 2
Avatar for L-x
L-x
12
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=integrate+cos+%284*%28x-3%29%5E2%29

But yeah, I'm expecting a typo in the OP
(edited 11 years ago)
I tried this on Maple and my laptop caught fire
Reply 4
Avatar for SubAtomic
SubAtomic
11
Pic from mathcad attached, hope this helps.

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

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.
(edited 11 years ago)
tsr 1.PNG7.2KB
A simple change of variables can reduce this to

Unparseable latex formula:

\include{bigint} \[ \int \frac{cos(x^2)}{\sqrt{a}} \mathfrac{d} x \]



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?
Reply 6
Avatar for haazu
haazu
OP
I am actually working on radars and I ended up with an integral attached.... can u please help me solve it
Integral.docx13.7KB
I can't seem to see that document - could you include a screenshot image?
Reply 8
Avatar for raheem94
raheem94
13
Original post by dantheman1261
I can't seem to see that document - could you include a screenshot image?


I don't suppose the jj refers to −1 \sqrt{-1} by any chance?
Reply 10
Avatar for haazu
haazu
OP
yes unfortunately it does, j(or i) is sqrt(-1)

Any hope that this can be solved?
After trying a few things I can't see a way - the tai t_{ai} and thi t_{hi} 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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