sinus integral

Moubinool

I think about this one, probably well known

Compute $\int_{0}^{+\infty}\frac{\sin(2004x)\sin(2005x)\sin(2006x)}{x}dx$

**Posted:** Fri Jan 14, 2005 2:43 pm

Kent Merryfield

$\int_0^{\infty}\frac{\sin(ax)}x\,dx=\frac{\pi}2$ for all $a>0.$

The basic challenge of Moubinool's problem is find a way, with trigonometric identities, to use this fact.

**Posted:** Fri Jan 14, 2005 3:56 pm

fredbel6

i'd say write the denominator as

-1/4*sin(6015*x)+(1/4)*sin(2005*x)+1/4*sin(2007*x)+1/4*sin(2003*x)
by using simpson twice

and then we get Pi/2 * (-1/4+1/4+1/4+1/4)=Pi/4

or is this too complicated?

**Posted:** Sat Jan 15, 2005 2:12 am