text: This area has to be separated into two parts because from 0 to Pi/6 the curve y = cosx is on top and\nfrom Pi/6 to Pi/2 the curve y = sin(2x) is on top\nArea = \nint(cosx-sin(2x)),0 to Pi/6 +\nint(sin(2x)-cosx), Pi/6 to Pi/2\n= sinx + (1/2)cos(2x) from 0 to Pi/6 +\n-(1/2)cos(2x) - sinx from Pi/6 to Pi/2\n= [sin(Pi/6) + (1/2)cos(Pi/3) - (sin(0) +(1/2)cos(0))] +\n[sin(Pi/2) + (1/2)cos(Pi) - (-sin(Pi/6) +(1/2)cos(Pi/3))] \n= [(1/2) + (1/2)(1/2) - (0 + 1/2)]\n+[1 + -1 - (-1/2 + (1/2)(1/2)}]\n= [1/2 + 1/4 - 1/2] - [-1/2 + 1/4]\n= 1/4 - (-1/4)\n= 1/2\nEdit: I verified this on my calculator.