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Integration

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    Can anyone please tell me how to integrate

    cos(a(t-b)^2) w.r.t t where a and b are constants
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    (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+
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    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
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    I tried this on Maple and my laptop caught fire
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    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.
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    A simple change of variables can reduce this to

     \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?
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    I am actually working on radars and I ended up with an integral attached.... can u please help me solve it
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  1. File Type: docx Integral.docx (13.4 KB, 33 views)
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    I can't seem to see that document - could you include a screenshot image?
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    (Original post by dantheman1261)
    I can't seem to see that document - could you include a screenshot image?
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    I don't suppose the j refers to  \sqrt{-1} by any chance?
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    yes unfortunately it does, j(or i) is sqrt(-1)

    Any hope that this can be solved?
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    After trying a few things I can't see a way - the  t_{ai} and  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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Updated: July 13, 2012
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