The curve y=sinx for π≤x≤2π lies below the x-axis.
At x=π: sin(π)=0
At x=23π: sin(23π)=−1
At x=2π: sin(2π)=0
Since the curve is below the x-axis, ∣sinx∣=−sinx in this interval.
Area =∫π2π∣sinx∣dx
Area =∫π2π(−sinx)dx
The integral of −sinx is cosx.
∫(−sinx)dx=cosx
Applying limits from π to 2π:
Area =[cosx]π2π
Area =cos(2π)−cos(π)
Area =1−(−1)
Area =2
Therefore, the area bounded by the curve y=sinx and the x-axis for π≤x≤2π is 2 square units.