Can you evaluate $$\int\sin(x^2)\mathrm{d}x \quad ?$$
I have tried substituting $p=x^2$ as well as integrating by parts, but then I came across an answer here which says that there is no way of working it out without using a computer.
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It's a non-trivial integral if I remember correctly. – Archaick Apr 17 '15 at 13:38
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1look for "Fresnel Integral" – Mosk Apr 17 '15 at 13:38
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it is this kind of integral $\sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} x\right)$ – Dr. Sonnhard Graubner Apr 17 '15 at 13:40
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It would be quite mean if the university asked us this in a test, because there is no solution! – ahorn Apr 17 '15 at 13:41
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A computer will not be more nor less successful as there is no closed formula using elementary functions. An educated mathematician will immediately recognize a Fresnel integral. If you mean "requires numerical methods", these can also be carried out by hand. – Apr 17 '15 at 14:08
