The curve y2+2y−x=0 and the vertical line x=2 bound a finite planar region S.
(a) Express x explicitly as a function of y using the equation y2+2y−x=0.
(b) Determine the exact y–coordinates of all intersection points of the curve with the line x=2.
(c) Using your results from parts (a) and (b), set up a definite integral with respect to y whose value equals the area of S, then evaluate the integral to obtain the exact area.