The above figure consists of a rectangle with a semicircle cut out of one end and added to the other end, where is the width of the rectangle, and the curved length of a semicircle is .
To calculate the area of the shaded figure, Svatejas applies the disc method as follows:
Consider the axis of integration to be the semicircular arc, which has length . For each horizontal strip, we have an area element (technically length element) of . Hence, the area is
What is the area of the shaded figure?