I am trying to figure out how to represent the integral [from 0 to 1] of cos(x^2) using a sum of a series. I know term by term integration/differentiation, i tried substitution but it didnt work.Any ideas for how to approach the problem?
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Use https://math.stackexchange.com/questions/469885/the-limit-of-a-sum-sum-k-1n-fracnn2k2/469886#469886 – lab bhattacharjee May 05 '17 at 13:09
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1Sorry for my ignorance but i cant seem to understand how that post helps. – dvd280 May 05 '17 at 13:17
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What's $f(x)$ here, then what should be $$f\left(\dfrac rn\right)$$ – lab bhattacharjee May 05 '17 at 13:18
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Hint: The primitive of the function is $\sqrt{\frac{\pi}{2}}C(\sqrt{\frac{2}{\pi}}x)$. Where C is the Fresnel Integral, wich you need to evaluate. – alexp9 May 05 '17 at 13:33
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Hint: $$\cos(x) = \sum_{n=0}^\infty \frac{(-1)^kx^{2k}}{(2k)!}$$
Replace all of the $x$ with $x^2$, and then integrate term by term.
NNN
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