# 1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but

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1. ## calculus

1. Find the volume V obtained by rotating the region bounded by the curves about the given axis. y = sin(x), y = 0, π/2 ≤ x ≤ π; about the x−axis 2. Find the volume V obtained by rotating the region bounded by the curves about the given axis. y = 3

2. ## Calculus-Area between curves

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 2y=4*sqrt(x) , y=5 and 2y+4x=8 please help! i've been trying this problem the last couple days, even asked a TA for help,

3. ## Calculus

Find the number b such that the line y = b divides the region bounded by the curves y = x2 and y = 4 into two regions with equal area.

4. ## Calculus

Find the area of the region bounded by the curves y = sin x, y = csc^2x, x = pi/4, and x = (3pi)/4.

5. ## calculus

1. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = ln(5x), y = 1, y = 3, x = 0; about the y-axis 2. Use the method of cylindrical shells to find the volume V generated by rotating the

1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate, the integral which gives

7. ## calc

Find the centroid of the region bounded by the given curves. y = 2 sin 3x, y = 2 cos 3x, x = 0, x = π/12

8. ## Calculus

Find the number b such that the line y = b divides the region bounded by the curves y = 4x2 and y = 1 into two regions with equal area. (Round your answer to two decimal places.)

9. ## calc

Find the area of the region bounded by the curves y equals the inverse sine of x divided by 4, y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative.

10. ## Calculus (Area Between Curves)

Find the area of the region IN THE FIRST QUADRANT (upper right quadrant) bounded by the curves y=sin(x)cos(x)^2, y=2xcos(x^2) and y=4-4x. You get: a.)1.8467 b.) 0.16165 c.) 0.36974 d.) 1.7281 e.) 0.37859

11. ## calculus

Find the number b such that the line y = b divides the region bounded by the curves y = 16x2 and y = 9 into two regions with equal area. (Round your answer to two decimal places.)

12. ## Calculus

Find the number a such that the line x = a divides the region bounded by the curves x = y^2 − 1 and the y-axis into 2 regions with equal area. Give your answer correct to 3 decimal places.

13. ## calculus 2

Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves. (Round your answer to two decimal places.) y = 8x^2− 3x, y = x^3−8x+ 2

14. ## Calculus (Area Between Curves)

Find the area of the region bounded by the curves y^2=x, y-4=x, y=-2 and y=1 (Hint: You'll definitely have to sketch this one on paper first.) You get: a.) 27/2 b.) 22/3 c.) 33/2 d.) 34/3 e.) 14

15. ## Calculus Help Please Urgent!!!

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5x^2, y = 5x, x ≥ 0; about the x-axis V = ??? Sketch the region

16. ## Calculus

Find the area of the region bounded by the curves of y=sin^-1(x/4), y=0, and x=4 obtained by integrating with respect to y. Your work must include the definite integral and the anti-derivative. I am really confused on this question. I graphed all of the

17. ## Calculus

Let f be the function given by f(x)=(x^3)/4 - (x^2)/3 - x/2 + 3cosx. Let R be the shaded region in the second quadrant bounded by the graph of f, and let S be the shaded region bounded by the graph of f and line l, the line tangent to the graph of f at

18. ## calculus

Consider the curves y = x^2and y = mx, where m is some positive constant. No matter what positive constant m is, the two curves enclose a region in the first quadrant.Without using a calculator, find the positive constant m such that the area of the region

19. ## calculus

Find the area bounded by {y=x2−4 y=4−x2 • sketch the region described • determine any intersection point(s) for the curves (show work!!) • write out the integral(s) that will calculate the area • determine the area (may use a calculator)

20. ## Calculus ll - Volumes

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y=e^(-x), y=1, x=2; about y=2.

21. ## calculus

Find the area of region bounded by the curves y=sin(pi/2*x)and y=x^2-2x.

22. ## Calculus

Find the area of the region bounded by the curves y=12-x^2 and y=x^2-6. Hint:The answer should be a whole number.

23. ## calculus

1. Find the area of the region bounded by f(x)=x^2 +6x+9 and g(x)=5(x+3). Show the integral used, the limits of integration and how to evaluate the integral. 2. Find the area of the region bounded by x=y^2+6, x=0 , y=-6, and y=7. Show all work required in

24. ## calculus

what is the area of the region bounded by the curves y=x^2 , y=8-x^2 , 4x-y+12=0

25. ## Calculus

Find the area of the region bounded by the curves y = x^(-1/2), y = x^(–2), y = 1, and y = 3. a) (1/2)(3)^1/2 + (4/3) b) 2*(3)^1/2 - (8/3) c) (1/2)(3)^1/2 - (32/3) d) 2*(3)^1/2 - (32/3) e) (8/3) - 2*(3)^1/2 So one thing that is throwing me off on this

26. ## calculus

find the centroid of the plane region bounded by the curves y = cos x, y=sinx, x=0,

27. ## calculus

10). Find the area of the region bounded by the graph of f(x)=4lnx/x, y=0, x=5.8 11). Find the area of the region bounded by x=y^2-1y, x=0

28. ## calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the line x=-3 y=x^2, x=y^2

29. ## Calculus

find the area of the region bounded by the curves y=x^2-1 and y =cos(x)

30. ## Calculus

Find the area of the region in the first quadrant bounded by the curves y=sin(x)cos^2(x), y= 2xcos(x^2), and y=4-4x a. 1.8467 b. 0.16165 c. 0.36974 d. 1.7281 e. 0.37859

31. ## cal 2

Find the number b such that the line y = b divides the region bounded by the curves y = x2 and y = 16 into two regions with equal area. (Round your answer to the nearest hundredth.)

32. ## calculus

Consider the graphs of y = 3x + c and y^2 = 6x, where c is a real constant. a. Determine all values of c for which the graphs intersect in two distinct points. b. suppose c = -3/2. Find the area of the region enclosed by the two curves. c. suppose c = 0.

33. ## Calc

Find the number b such that the line y = b divides the region bounded by the curves y = 4x2 and y = 16 into two regions with equal area. (Round your answer to two decimal places.)

34. ## Calculus

Find the area of the region bounded by the line y=3x and y= x^3 + 2x^2? and find the area of the region bounded by the curve y=e^2x -3e^x + 2 and the x-axis?

35. ## Calculus

Let A be the region bounded by the curves y = x^2-6x + 8 and y = 0. Find the volume obtained when A is revolved around the Y-AXIS

36. ## Calculus

We're learning disks, shells, and cylinders in school but we have a substitute and I've been trying to teach this to myself. Can you check them please? =) Thank you! 1) Find the volume of the solid formed when the region bounded by curves y=x^3 + 1, x= 1,

37. ## Calculus

We're learning disks, shells, and cylinders in school but we have a substitute and I've been trying to teach this to myself. Can you check them please? =) Thank you! 1) Find the volume of the solid formed when the region bounded by curves y=x^3 + 1, x= 1,

38. ## math, calculus

1. Consider the region bounded by the curves y=|x^2+x-12|, x=-5, and x=5 and the x-axis. A. Set up a sum of integrals, not containing an absolute value symbol, that can be used to find the area of this region. B. Find the area of the region by using your

39. ## Calculus

1. Find the area of the region bounded by the curves and lines y=e^x sin e^x, x=0, y=0, and the curve's first positive intersection with the x-axis. 2. The area under the curve of y=1/x from x=a to x=5 is approximately 0.916 where 1

40. ## Math

The curves y=sinx and y=cosx intersects twice on the interval (0,2pi). Find the area of the region bounded by the two curves between the points of intersection.

41. ## Math

The curves y=sinx and y=cosx intersects twice on the interval (0,2pi). Find the area of the region bounded by the two curves between the points of intersection.

42. ## calculus

Sketch the region bounded by the curves y = x^2, y = x^4. 1) Find the area of the region enclosed by the two curves; 2) Find the volume of the solid obtained by rotating the above region about the x-axis; 3) Find the volume of the solid obtained by

43. ## Calculus

The region R is the region in the first quadrant bounded by the curves y=x^ 2 -4x+ 4, x = 0 , and x = 2, as seen in the image attached below: ibb.co/WgrRRRL Find a value h such that the vertical line x = h divides the region R into two regions of equal

44. ## calculus

find the area of the region bounded by the curves f(x)=x-x^3 ; g(x)=x^2-x ; over [0,1]

45. ## calculus

Find the area of the region bounded by the curves y=x^2 & y=2x???

46. ## math

find the area of region R bounded by the curves y=3x , x=2y and 2x+y=5

47. ## Calculus

Find the area of the region bounded by the curves y=x^2 - 2x and y= x + 4

48. ## calc

find the area under the region bounded by the curves y=x^2-3 and y=2x.

49. ## integral calculus

FIND THE AREA OF THE REGION BOUNDED BY THE CURVES Y= X^2 + 4X + 3 AND Y= x-1.

50. ## Kenya water

Find the area of the region bounded by the curves y=xsinx and y=(x-2)^2

51. ## Math

How do I find the area of the region bounded by the curves y = e^x, y = e^-x, x= -2, and x = 1? Even if you could just help me in getting started it would be a HUGE help. Thanks!

52. ## Calculus

find area of the region bounded by the curves y=x^2-1 and y=cos(x). give your answer correct to 2 decimal places.

53. ## Ap Calculus

Find the area of the region bounded by the curves y=x^2-1 and y=cos(x). Give your answer correct to 2 decimal places

54. ## math-calculus 2

Consider the given curves to do the following. 64 y = x^3, y = 0, x = 4 Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 1.

55. ## MATH

Region A that on xy-plane is bounded by two (2) curves and a line. The curves are y=x^3-2x+3 and y=-x^2+3 while the line is x=0. It is located in the first quadrant of xy-plane. Determine the area of region A.

56. ## Calculus

Calculate the area of the bounded region between the curves y^2=x and 3y = -3y + 9 ?

57. ## AP Calculus

Find the area of the region bounded by the curves y = sin^-1(x/2), y = 0, and x = 2 obtained by integrating with respect to y. Please include the definite integral and the antiderivative.

58. ## Calculus

Find the area of the region bounded by the curves y = sin^-1(x/4) , y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative.

59. ## Calc

Find the area of the region bounded by the curves y = sin^-1(x/6), y = 0, and x = 6 obtained by integrating with respect to y. Please include the definite integral and anti-derivative.

60. ## calculus

Find the number b such that the line y = b divides the region bounded by the curves y = 16x2 and y = 9 into two regions with equal area. (Round your answer to two decimal places.)

61. ## Calc

Find the area of the region bounded by the curves y2 = x, y – 4 = x, y = –2, and y = 1. So far I have found that the area of the trapezoid which is 13.5. But for the other two areas I cannot find them. They could be: 27/2 22/3 33/2 34/3 14 I believe

62. ## calc

Find the number a such that the line x = a divides the region bounded by the curves x = y^2 − 1 and the y-axis into 2 regions with equal area. Give your answer correct to 3 decimal places.

63. ## calculus

A region is bounded by the function y=2x^2+3 and the x-axis over the interval(0,2). Sketch the graph of the bounded region. Use the limit process to find the area of the bounded region. Explain the step in this limit process. Please explain all procedured

64. ## Calculus

Find the area of the region which is bounded by the polar curves theta =pi and r=2theta 0

65. ## Math

Find the area of the region which is bounded by the polar curves theta =pi and r=2theta 0

66. ## Maths

Find the area of the region which is bounded by the polar curves theta =pi and r=2theta 0

67. ## Calculus

Find the area of the region which is bounded by the polar curves theta =pi and r=2theta 0

68. ## Calculus

Find the area of the region which is bounded by the polar curves theta =pi and r=2theta 0

69. ## Calculus

Find the area of the region which is bounded by the polar curves theta =pi and r=2theta 0

70. ## Calculus

Consider the region bounded by the curves y=e^x, y=-e^x, and x=1. Use the method of cylindrical shells to find the volume of the solid obtained by rotating this region about the y-axis.

71. ## calculus

Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = x^3 and y = x.? I know how to use the midpoint rule to get the area under a curve but I'm confused on how to get the area between the two curves. Do I subtract them

72. ## calculus

Determine the exact value for the constant k such that the area of the region bounded by the curves y=x and y=kx^2 is equal to 2/3 sq units. Any help is appreciated.

73. ## calculus wxmaxima

does anyone know how to approximate the are and circumfrence of the region bounded by the given curves y=cos(x^2 +(100493/100000)), y=1+x-X^2 i already did the area but i need help with the circumference

74. ## calculus

use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. sketch the region and a typical shell. x=1+y^2, x=0, y=1, y=2

75. ## math

If the curves of f(x) and g(x) intersect x=a and x=b and if f(x)>g(x)>0 for all x on (a,b) then the volume obtained when the region bounded by the curves is rotated about the x-axis is equal to

76. ## math

region bounded by the parabolas y=x^2 and y=6x-(x^2) is rotated about the x-axis so that a vertical line segment cut off by the curves generates a ring. find the value of x for which we obtain the ring of largest area

77. ## Calculus

Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = x^3 and y = x. I just need to know how to use the midpoint rule when the area is between two curves instead of under a curve. Help please.

78. ## calculus

Find the continuity of the region bounded by the two curves. y=x^2 and y=3x?

79. ## calculus

find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. sketch the region and a typical disk or washer. y^2=x, x=2y; about the y-axis i am confused because i do not know how to set it up because

80. ## geometry

Consider the region in Quadrant 1 totally bounded by the 4 lines: x = 3, x = 9, y = 0, and y = mx (where m is positive). Determine the value of c such that the vertical line x = c bisects the area of that totally bounded region. Needless to say, your first

81. ## math

Consider the region in Quadrant 1 totally bounded by the 4 lines: x = 3, x = 9, y = 0, and y = mx (where m is positive). Determine the value of c such that the vertical line x = c bisects the area of that totally bounded region. Needless to say, your first

82. ## geometry

Consider the region in Quadrant 1 totally bounded by the 4 lines: x = 3, x = 9, y = 0, and y = mx (where m is positive). Determine the value of c such that the vertical line x = c bisects the area of that totally bounded region. Needless to say, your first

83. ## calculus

Let A be the region bounded by the curves y=x^2-6x+8 and y=0, find the volume when A is revolved around the x-axis

84. ## math

find volume when the region bounded by the curves y = Ln(x), y = 2, and x = 1 is revolved around the line y = −2.

85. ## Calculus

Let A be the region bounded by the curves y = x^2-6x + 8 and y = 0. Find the volume obtained when A is revolved around the Y-AXIS

86. ## math

Consider the region bounded by the curves y=5 and y=5 and y = x +4/x. set up the integral that would be used to determine the volume if the region was revolved about x = -1

87. ## calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x+y=4,x=5−(y−1) 2 ;

88. ## Calc

find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis y=x^2+1; y=9-x^2; about y=-1

89. ## Calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line: y=x, y=x^(1/2); about x=2

90. ## Calc2

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = x2, y = 1; about y = 6

91. ## K

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 3e^(-x), y = 3, x = 2; about y = 6

92. ## calculus

Find the volume of the solid obtained by rotating the region bounded by the curves y=x^6, y=1 about the line y=4

93. ## calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=1/x^4, y=0, x=2, x=9; about y=–5

94. ## calculus 2

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x, y = 0, x = 2, x = 6; about x = 1

95. ## calculus one

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^4,y=1; about y=5

96. ## Calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^2,y=1; about y=7

97. ## Calculus

find volume of solid obtained by rotating region bounded by curves y=x and y=sq.rt x, about line x=2

98. ## calculus

find the volume of the solid obtianed by rotating the region bounded by the given curves about the line x=6 x=y^2 , x=1

99. ## Cal

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=1/x^2, y=0, x=4, x=5; about y=−2

100. ## calculus

Find the volume generated by revolving about the x-axis the region bounded by the following curves y=sqrt/(4x+3),x=0,x=4, and y=0. (Use "pi" for π).