Solve these problems.

6.2 Exercises 1-12 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. 1. y = 2 - {x, y = 0, x = 1, x =2; about the x-axis 2. y = 1 - x', y =0; about the x-axis 3. x = 2vy, x =0, y =9; about the y-axis 4. y = Inx, y = 1, y = 2, x =0; about the y-axis 5. y = x', y = x, x20; about the x-axis 6. y = 1x', y = 5 -x2; about the x-axis 7. y' = x, x = 2y; about the y-axis 8. y = 1x', x = 2, y =0; about the y-axis 9. y = x, y = vx; about y = 1 10. y = e-*, y = 1, x = 2; about y = 2 11. y = 1 + sec x, y = 3; about y = 1 12. y = x, y = vx; about x = 2 13-18 The region enclosed by the given curves is rotated about the specified line. Find the volume of the resulting solid. 13. y = 1/x, x = 1, x = 2, y =0; about the x-axis 14. x = 2y - y', x = 0; about the y-axis 15. x - y = 1, y = x' - 4x + 3; about y = 313-18 The region enclosed by the given curves is rotated about the specified line. Find the volume of the resulting solid. 13. y = 1/x, x = 1, x = 2, y =0; about the x-axis 14. x = 2y - y', x = 0; about the y-axis 15. x - y = 1, y = x - 4x + 3; about y = 3 16. x = y', x = 1; about x = 1 17. y = x3, y = vx; about x = 1 18. y = x3, y = vx; about y = 1 19-20 Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. 19. x3 - y' = 1, x = 3; about x = -2 20. y = cos x, y = 2 - cos x, 0 S x = 27; about y = 4