# Very quick question

1. Jun 20, 2005

### bomba923

$\forall n > 0,\;n \in \mathbb{R}$, does
$$\int\limits_n^\infty {\frac{{\sin x}} {x}dx}$$
converge? If so, to what?

2. Jun 20, 2005

### dextercioby

It's a function of "n".It converges for every possible "n".

$$\int_{n}^{\infty} \mbox{sinc} \ x \ dx =\frac{\pi}{2}-\mbox{Si}\ (x)$$.

Daniel.

3. Jun 20, 2005

### steven187

hello there

well I have attached a plot of the intergrand, as you would see the function converges to 0 and should be integrable

Steven

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4. Jun 20, 2005

### fourier jr

you can prove that it converges by multiplying the integrand by 1 (in this case pick x/x or x^2/x^2 or something) & use integration by parts, & then the comparison test. i don't think that helps find what it converges to but judging by the image it looks like it goes to 0.

5. Jun 21, 2005