Questions 25,32 please!
2.2 Double Integrals over General Regions 127 9-16. Regions of integration Sketch each region and write an 33-38. Regions of integration Sketch each region and write an iterated integral of a continuous function f over the region. Use the iterated integral of a continuous function f over the region. Use the order dy dx. order dx dy. 9. R = { (x, y): 0 S x = 1/4, sin x y s cos x} 33. The region bounded by y = 2x + 3, y = 3x - 7, and y = 0 10. R = { (x, y) : 0 5 x = 2, 3x2 sys -6x + 24} 34. R = { (x, y): 0= xsy(1- y) } 11. R = { (x, y ) : 1 5 x 5 2, x + 1 sys 2x + 4} 35. The region bounded by y = 4 - x, y = 1, and x = 0 12. R = { ( x , y ) : 0 S x 5 4, x2 sys 8Vx} 36. The region in quadrants 2 and 3 bounded by the semicircle with radius 3 centered at (0, 0) 13. R is the triangular region with vertices (0, 0), (0, 2), and (1, 0). 37. The region bounded by the triangle with vertices (0, 0), (2, 0), 14. R is the triangular region with vertices (0, 0), (0, 2), and (1, 1). and ( 1, 1) 15. R is the region in the first quadrant bounded by a circle of radius 38. The region in the first quadrant bounded by the x-axis, the line 1 centered at the origin. x = 6 - y, and the curve y = Vx 16. R is the region in the first quadrant bounded by the y-axis and the 39-46. Evaluating integrals Evaluate the following integrals as they parabolas y = x and y = 1 - x2 are written. 17-26. Evaluating integrals Evaluate the following integrals as they are written. 39. MS, dady 40. 18 . 41. J. 2ry dexdy 42 . 19 . 20 . S . S (x - 1) dy de 43. 44 . 21. 22 . 45. 23 . 24. 46. 25 . 26. 47-52. Evaluating integrals Evaluate the following integrals. A sketch is helpful. 27-30. Evaluating integrals Evaluate the following integrals. A sketch is helpful 47. JUR 12y dA; R is bounded by y = 2 - x, y = VI, and y = 0. 27. JRXy dA; R is bounded by x = 0, y = 2x + 1, and 48. JURY2 dA; R is bounded by y = 1, y = 1 - x, andy = x - 1. y = -2x + 5. 49. JR 3xy dA; R is bounded by y = 2 - x, y = 0, and 28. JUR (x + y) dA; R is the region in the first quadrant bounded by x = 4 - y2 in the first quadrant. x = 0, y = x2, and y = 8 - x2. 50. SIR (x + y) dA; R is bounded by y = [x| and y = 4. JURY? dA; R is bounded by x = 1, y = 2x + 2, and 51. JUR 3x2 dA; R is bounded by y = 0, y = 2x + 4, and y = x3. - 1. 30. JR XZy dA; R is the region in quadrants 1 and 4 bounded by the 52. SIR x2 y dA; R is bounded by y = 0, y = Vx, and y = x - 2. semicircle of radius 4 centered at (0, 0). 53-56. Volumes Use double integrals to calculate the volume of the following regions. 31-32. Regions of integration Write an iterated integral of a continu- ous function f over the region R shown in the figure. 53. The tetrahedron bounded by the coordinate planes 31. (x = 0, y = 0, z = 0) and the plane z = 8 - 2x - 4y 32. 20 - 54. The solid in the first octant bounded by the coordinate planes and (9, 18) x = V25 - 12 the surface z = 1 - y - x2 10 - y = 2x 55. R The segment of the cylinder x2 + yz = 1 bounded above by the R /y = 3x - 9 plane z = 12 + x + y and below by z = 0 10 * 56. The solid beneath the cylinder z = y and above the region (3, -4) R = { ( x, y ) : 0 s y = ], y s x= 1 } y = -3x + 5 _ Dashboard pop Cal 9
