Let g(x)=∣sinx∣ on the interval 0≤x≤2π.
a. (i) Express g(x) as a piecewise‐defined function without the absolute value sign over the interval 0≤x≤2π.
b. (ii) Obtain a single antiderivative G(x) that is valid for all x in [0,2π] by integrating each piece and stitching the results together so that G(x) is continuous on the whole interval.
c. (iii) Using the antiderivative found in part (ii), compute G(2π)−G(0) without re‐integrating.