Integration of sin x^2

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

#Calculus #Trigonometric #Integral #Frescel

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

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: $\displaystyle S(x) = \int_0^x \sin(t^2) \, dt = \sum_{n=0}^\infty (-1)^n \frac{x^{4n+3}}{(2n+1)!(4n+3)}$ .

Pi Han Goh - 5 years, 12 months ago

@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

Aman Rajput - 5 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$