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It is sometimes very difficult to evaluate an integral, but easy enough to verify if the solution is correct. Seems to me like it should at least be np, but my understanding of the concept is limited and I might be missing something

Edit: just to be clear, I am curious about the complexity of an algorithm which finds an anti derivative of a function in order to solve an indefinite integral, not computing a numerical approximation to a definite integral.

kevingregg
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  • I remember reading that integrals can be used to perform computation, but I don't remember where. I know you can use Cauchy integrals to calculate the n'th derivative of an analytic function at a point, but not much more than that. This way you can generate the nth Fibonacci number if you perform a Cauchy integral to find the n'th derivative of the generating function of the Fibonacci sequence. – NovaDenizen Sep 23 '14 at 01:54

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Integrals are typically interpolated computing an approximation of the actual value of the integral and these algorithms are definitely not np, nor np hard or np complete. Computation of an approximation of any a-priory known precision is polynomial.

Ivaylo Strandjev
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  • What I am really curious about is an algorithm that found an exact antiderivative function instead of a numerical approximation of a definite integral. Does such an algorithm even exist? – kevingregg Feb 27 '14 at 11:03
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    Not all integrals lead to antiderivative that is a well known function. There may be some algorithms able to solve some simple integrals but I am absolutely sure there is no algorithm able to solve **any** integral – Ivaylo Strandjev Feb 27 '14 at 11:36