integral of sin(x)sin(x+1)

Question

Integral (from 0 to 2pi) [Sin(x)*Sin(x+1)] dx

Thank you

Answer 1

set up the integral of sin(x)sin(x+1) as sin(x){ sin(x)cos(1) - cos(x)sin(1) }= cos(1)sin2(x) = sin(1)sin(x)cos(x)

both integrals are straightforward and the integration should be

cos(1)(1/2){ x - (1/2)sin(2x) } + (1/2)sin(1)sin2(x) } from zero to pi

I get .54pi (remember that cos(1) is cosine of 1 radian etc)