do the circled ones please

In Exercises 31 - 34, find a value c guaranteed by the Mean In Exercises 47 - 50, an acceleration function of an object Value Theorem. moving along a straight line is given. Find the change of the object's velocity over the given time interval. 31. x2 dx Exercises 5.4 47. a(t) = -32ft/s on [0, 2] Terms and Concepts 18 . dx 32 . * dx 48. a(t) = 10ft/s on [0, 5] 1. How are definite and indefinite integrals related? . What constant of integration is most commonly used when 19. 2 dx 3 3 . edx 19. a(t) = t ft/s on [0, 2] evaluating definite int 3. T/F: If f is a continuous function, then F(x) = / f(t) at is 20 2 1 dx 34 . ( V x dx 50. a(t) = cost ft/s' on [0, 7] also a continuous function. . The definite integral can be used to find "the area under a In Exercises 35-40, find the average value of the function on In Exercises 51 - 54, sketch the given functions and find the curve." Give two other uses for definite integrals. 21 . * dx the given interval. area of the enclosed region. 35. f(x) = sin x on [0, 7 /2] Problems 51. y = 2x, y = 5x, and x = 3. 22 . * 2 dx 36. y = sin x on [0, 7] In Exercises 5 - 28, evaluate the definite integral. 52. y = -x + 1, y = 3x + 6, x = 2 and x = -1. 37. y = x on [0, 4] 5. ( 3X ] - 2x + 1 ) dx 23 . * dx 38. y = x on [0, 4] 53. y = x2 - 2x + 5, y=5x -5. 6. / ( x - 1) 2 dx 39. y = x on [0, 4] 54. y = 2x2 + 2x - 5, y = x2+ 3x + 7. 24 . * 100 dx 7 . [ ( x - x ) ox 40. g(t) = 1/t on [1, e] In Exercises 55 - 58, find F' (x). 8 . / cosxox 25 . dx In Exercises 41 - 46, a velocity function of an object moving along a straight line is given. Find the displacement of the object over the given time interval. 55. F(x) = 9 . "sec x dx 26. 3 dx 41. v(t) = -32t + 20ft/s on [0, 5] 10 . dx 42. v(t) = -32t + 200ft/s on [0, 10] 56. F ( x ) = +3 dt 27 . O dx 11 . 5 " dx 43. v(t) = 10ft/s on [0, 3]. 57. F ( x ) = (+ + 2 ) at 44. v(t) = 2'mph on [-1, 1] (12) 1, (4 - 2x ) dx 28 . CSCx cot x dx 45. v(t) = cost ft/s on [0, 37 /2] 58 . F ( x ) = sint at 13 . ( 2 cos * - 2 sin * ) dx 29 Explain why : 46. v(t) = Vtft/s on [0, 16] (a ) x dx = 0, when n is a positive, odd integer , and 15 . Vidt 16) X dx = 2 / *" dx when n is a positive , even integer . 17 . V X dx 30. Explain why 10 + 2 7 sint dt = 0 for all values of a. 46 voOOGA_ 0