Region R is bounded by the parabola x=y2 and the vertical line x=4.
a. Sketch or describe the graph of R, clearly indicating all intersection points with their coordinates.
b. Determine whether calculating the area of R by integrating with respect to x or with respect to y requires fewer definite integrals. Justify your answer based solely on geometric considerations of the region.
c. Write, but do not evaluate, a single definite integral that represents the area of R using the variable you identified in part (b).