Find the area bounded by the curve and the lines y=sinx, y= 1/2, x=5pi/6 and x=pi/6

Answer 1

Note that sin(5pi/6)=sin(pi/6)=1/2.
Area=Integral(from pi/6 to 5pi/6)(sinx-1/2)dx=(-cosx-x/2)I(pi/6 to 5pi/6)=
(-cos(5pi/6)-5pi/12)-(-cos(pi/6)-pi/12)=
=sqrt(3)-pi/3=0.685