v4sin' t + cos2 t dt Jo 9.69. Since the ellipse is inscribed in a circle of radius 2 and circumscribes a circle of radius 1, we expect the length of the ellipse to be between 2T(2) 12.57 and 2(1) 6.28, so the value of 9.69 is reasonable Exercises and Problems for Section 8.2 Exercises 1. (a) The region in Figure 8.29 is rotated around the 2. (a) The region in Figure 8.30 is rotated around the z- axis. Using the strip shown, write an integral giving the volume. axis. Using the strip shown, write an integral giving the volume. (b) Evaluate the integral. (b) Evaluate the integral. y=2a 6 Figure 8.30 Figure 8.29