## lovekblue Group Title Need help in integral area involve 3d objects one year ago one year ago

1. lovekblue Group Title

2. Algebraic! Group Title

3. Algebraic! Group Title

ah I see those are multiple choices...

4. Algebraic! Group Title

did you get the 'sketch the region' one?

5. Algebraic! Group Title

basically just asking you to pick which of those areas is bounded by y=5, x=4 and the function...

6. Algebraic! Group Title

you there?

7. Algebraic! Group Title

the first choice is bounded by y=10, x=4 and the function... the second choice is bounded by y=10, x=0, x=4 and the function...

8. lovekblue Group Title

yes i am here..

9. lovekblue Group Title

10. lovekblue Group Title

For the first picture, i think it is the last one for the 2nd picture, i am thinking either 1st or 4th one , what do u think ?

11. Algebraic! Group Title

naw, the last picture is bounded by x=0 y=0 and the function...

12. Algebraic! Group Title

(and x=4)

13. lovekblue Group Title

so for the first picture, u also think is the last one?

14. lovekblue Group Title

for my function, x is not 0 u mean?

15. Algebraic! Group Title

just trace around each of those red regions and see what functions or lines your tracing...

16. Algebraic! Group Title

what lines do you trace for the last choice?

17. Algebraic! Group Title

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18. lovekblue Group Title

yea, that's what i have too. dont really know how i got that..but yeah.. Do you possibly know how to volume the volume of this?

19. Algebraic! Group Title

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20. Algebraic! Group Title

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21. lovekblue Group Title

dont u need to integrate the area function to volume , and then something to do with the height..?

22. Algebraic! Group Title

so... is that the region described in your problem statement??

23. lovekblue Group Title

yes

24. Algebraic! Group Title

really? your problem statement makes no mention of x=0 or y=0 ...

25. Algebraic! Group Title

it does mention y=5 however...

26. lovekblue Group Title

well, but it says rotate about y= 10, and y= 5

27. Algebraic! Group Title

naw..

28. lovekblue Group Title

then u can kinda know there is a hole in between

29. lovekblue Group Title

umm..wait..so which picture do you think it is for the first set of picture? i thought we have the same answer

30. Algebraic! Group Title

the region is bounded by x=4 y=5 and y=5e^-x

31. Algebraic! Group Title

like I said trace the boundary of the regions you have been given to find which one works with that description..

32. Algebraic! Group Title

there's no point in guessing here... even though this is multiple guess

33. lovekblue Group Title

i still think is the last one..

34. lovekblue Group Title

that's why i want to know which one u think it is

35. Algebraic! Group Title

why is it the last one..

36. Algebraic! Group Title

are you talking about the first part or the second part?

37. lovekblue Group Title

first part ..

38. Algebraic! Group Title

because if you do the first part correctly, the answer to the second part should be obvious

39. Algebraic! Group Title

ok..

40. lovekblue Group Title

so do you agree that it is either the bottom left or bottom right picture is correct due to the fact that given y=5

41. Algebraic! Group Title

then why are you saying it's the last region?

42. lovekblue Group Title

why is it not the last picture ..lol |dw:1352778179844:dw|

43. Algebraic! Group Title

did you see the sketches where I traced the bounding functions??

44. Algebraic! Group Title

what are they??

45. lovekblue Group Title

the curve is y= 5e^-x , y =5 , x=4

46. Algebraic! Group Title

what functions bound the region in the last picture?

47. Algebraic! Group Title

hint: I already did it for you.

48. lovekblue Group Title

x=0, y=0..which i dont really get u ..o_o

49. Algebraic! Group Title

trace the boundary

50. Algebraic! Group Title

|dw:1352778560923:dw|

51. Algebraic! Group Title

what's that portion?

52. Algebraic! Group Title

say "y=0"

53. Algebraic! Group Title

|dw:1352778627593:dw|

54. Algebraic! Group Title

what's that portion?

55. lovekblue Group Title

are you trying to say that radius doesnt bound to x=0?

56. lovekblue Group Title

which it does indeed make sense when i look in the 2nd part

57. Algebraic! Group Title

I'd focus on the first part, if I were you..

58. Algebraic! Group Title

picking which region is bounded by y=5, x=4 and y= 5e^-x

59. lovekblue Group Title

i'm not sure what u mean by bounded..do you mean by starting from there？

60. Algebraic! Group Title

trace the boundary of each region

61. Algebraic! Group Title

like I did... for the last region pictured in your choices...

62. lovekblue Group Title

if i do what u did, then the answer will be the bottom left

63. Algebraic! Group Title

yes

64. lovekblue Group Title

but my question with that picture is.. don't u need to do 5- 5e^-t in order to get tht area?

65. Algebraic! Group Title

not necessarily..

66. Algebraic! Group Title

you'll be using washers probably, since you haven't learned about shells yet (I assume)...

67. Algebraic! Group Title

so the inner radius is 5 and the outer radius is 10-5e^-x

68. lovekblue Group Title

yea i didnt yet.. i didnt even learn these stuff much when my assignment is due 2 days after..

69. lovekblue Group Title

ya, i do get that part

70. Algebraic! Group Title

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71. lovekblue Group Title

is that region not what the last picture look like?

72. Algebraic! Group Title

for the second part... yep.

73. lovekblue Group Title

can i ask what does "region " mean..

74. Algebraic! Group Title

the red areas in the first part.

75. lovekblue Group Title

yea..what does that red area mean

76. lovekblue Group Title

is it like the path of rotation or something?

77. Algebraic! Group Title

no.

78. Algebraic! Group Title

it's the thing you're sweeping around the specified axis in order to generate a solid

79. Algebraic! Group Title

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80. Algebraic! Group Title

take that region as an example... it's a rectangle...

81. Algebraic! Group Title

rotate about the x axis and you sweep out a cylinder..

82. lovekblue Group Title

so it's kinda you are sweeping that region, and that sweeping motion generate the solid figure?

83. Algebraic! Group Title

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84. Algebraic! Group Title

yes, exactly.

85. lovekblue Group Title

okay thank you so so much!!!!!!

86. lovekblue Group Title

Do you still have time to guide me on filding the volume?

87. Algebraic! Group Title

the second multiple choice question? or a new question?

88. lovekblue Group Title

it's the same question. but it asks to find the volume

89. lovekblue Group Title

cuz finding the volume is actually the first part..but the graphing part seems easier so i skipped to that first ..

90. Algebraic! Group Title

sure... we are using the washers in the sketch (and in the last choice to the second question)

91. Algebraic! Group Title

92. Algebraic! Group Title

area of a washer will be pi( (10 - 5e^-x)^2 - 5^2 )

93. lovekblue Group Title

yea..that's all i have too.. not sure how to integrate that..

94. Algebraic! Group Title

$\pi \int\limits_{ }^{} (10-5e^{-x})^2 - 5^2 dx$

95. Algebraic! Group Title

$\pi \int\limits_{0}^{4} 75 -100e^{-x} +25e^{-2x} dx$

96. Algebraic! Group Title

that should be pretty easy to integrate...

97. lovekblue Group Title

oh ok..i didnt combine them.. ok thanks, i will try that out :)

98. lovekblue Group Title

@Algebraic! umm.. how can i leave it as exact numbers..?

99. lovekblue Group Title

i got pi ((300+10 e^-4 - 25/2 e^-8)- (10-25/2))