Question 345463
The value of the cosine function at the endpoints are,
{{{cos(pi/6)=sqrt(3)/2}}}
{{{cos(pi/3)=1/2}}}
The value of the function in between the endpoints is bounded by those values.
{{{1/2<=cos(x)<=sqrt(3)/2}}}
So then integrating,
{{{ (1/2)*int(1,dx,pi/6,pi/3) <= int ( cos(x), dx, pi/6, pi/3 ) <= (sqrt(3)/2)*int(1,dx,pi/6,pi/3)  }}}
{{{ (1/2)(pi/3-pi/6) <= int ( cos(x), dx, pi/6, pi/3 ) <= (sqrt(3)/2)(pi/3-pi/6) }}}
{{{pi/3-pi/6=(2pi)/6-pi/6=pi/6}}}
Substituting,
{{{ (1/2)(pi/6) <= int ( cos(x), dx, pi/6, pi/3 ) <= (sqrt(3)/2)(pi/6) }}}
{{{ highlight(pi/12 <= int ( cos(x), dx, pi/6, pi/3 ) <= (sqrt(3)/12)pi) }}}