Question

Finding Area by the Limit Definition In Exercises 47–56, use the limit process to find the area of the region bounded by the graph of the function and the x-axis over the given interval. Sketch the region. 47. y = - 4x + 5, [0, 1] 48. y = 3x - 2. [2,5] 49. y = x2 + 2, [0, 1] 50. y = 5x + 1, [0, 2] 51. y = 25 - x?, [1,4] 52. y = 4 - x? [-2, 2] 53. y = 27 - x, [1,3] 54. y = 2x - x, [0, 1] 55. y = x2 - x, [-1,1] 56. y = 2x3 - x?, [1, 2] Finding Area by the Limit Definition In Exercises 57–62, use the limit process to find the area of the region bounded by the graph of the function and the y-axis over the given y-interval. Sketch the region. 57. f(y) = 4y, 0 sy s 2 58. g(y) = y, 2 sy s 4 59. f(y) = y2. Os y s 5 60. y = 3y - ya, 2 sy s 3 61. g(y) = 4y2 - y, 1 = y 3 62. h(y) = y + 1, lsys 2 O Approximating Area with the Midpoint Rule In Exercises 63-68, use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the function and the x-axis over the given interval
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Answer 1

47 9 Area (A) aza lim din is y=0) stories n200 Ar= 6-9 y=f(1) =-44775 [01] s finida Limit definition of staid Ĉ famigax. = 1-0 = Xi = a + id =orilta f(xi) 5-42i = 5-464) = f(ni)su = (5-412C) as - 41 S (5-Hujan ĈI 높 5- Lain - til - hint y-5-44 ho : ] lim n 100 in ini - ''[26 - ''] 《ས "ས་ म ( n700 home (50 mg af let] [5-2(1++] = 5-2(1+to lim no 5-2 = 3 = 5-2(10) - sis-unar - -S/ 3 0