( 2xy'e) dy (using the tube method). y=0 B y = In(x) (a) Before evaluating the integrals, which volume do you think is A larger? Why? (b) Evaluate the integrals. Was your prediction in part (a) correct? Fig. 2: Comparing volumes 8.3 Integration By Parts Contemporary Calculus 36. Use the tube method to calculate the volume when the region between the x-axis and the graph of y = sin(x) for 0 s x s x is rotated about the y-axis