Question

Find the area of the region between the curves y=sin(x), y=sin(2x), x=0, x=pi/2

Answer 1

since we are asked to find the area between a region where parts of the integral are where \(\large \sin(2x)\ge \sin(x)\) and other parts where \(\large \sin(x) \ge \sin(2x)\) you have to split up the integral. \[\large A= \int\limits_{0}^{\pi/2} |\sin(2x)-\sin(x)|dx=A_{1}+A_{2}\] A1 refers to the first area of the integral, and A2 refers to the second area of the area