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# Integration of sin x^2

I don't know how to integrate this sin(x^2) . Can someone show me how to? Thanks

Note by Dollesin Joseph
1 year, 7 months ago

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@Dollesin Joseph Use this result: $$\displaystyle \int\limits_0^{\infty} \sin(x^n) dx = \sin(\frac{\pi}{2n})\frac{\Gamma(n+1)}{\Gamma(n)}$$..

that is only for these limits... other wise mention limits · 1 year, 5 months ago

You can't express this integral in terms of elementary functions. This integral is known as the Fresnel integral. You can express the integral as a power series instead: $$\displaystyle S(x) = \int_0^x \sin(t^2) \, dt = \sum_{n=0}^\infty (-1)^n \frac{x^{4n+3}}{(2n+1)!(4n+3)}$$. · 1 year, 7 months ago