## lovekblue 3 years ago Need help in integral area involve 3d objects

1. lovekblue

2. Algebraic!

3. Algebraic!

ah I see those are multiple choices...

4. Algebraic!

did you get the 'sketch the region' one?

5. Algebraic!

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

6. Algebraic!

you there?

7. Algebraic!

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

yes i am here..

9. lovekblue

I know the answer for the first picture already, not sure about the 2nd one @Algebraic!

10. lovekblue

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!

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

12. Algebraic!

(and x=4)

13. lovekblue

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

14. lovekblue

for my function, x is not 0 u mean?

15. Algebraic!

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

16. Algebraic!

what lines do you trace for the last choice?

17. Algebraic!

|dw:1352777609189:dw|

18. lovekblue

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!

|dw:1352777630991:dw|

20. Algebraic!

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21. lovekblue

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

22. Algebraic!

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

23. lovekblue

yes

24. Algebraic!

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

25. Algebraic!

it does mention y=5 however...

26. lovekblue

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

27. Algebraic!

naw..

28. lovekblue

then u can kinda know there is a hole in between

29. lovekblue

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!

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

31. Algebraic!

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

32. Algebraic!

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

33. lovekblue

i still think is the last one..

34. lovekblue

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

35. Algebraic!

why is it the last one..

36. Algebraic!

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

37. lovekblue

first part ..

38. Algebraic!

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

39. Algebraic!

ok..

40. lovekblue

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!

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

42. lovekblue

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

43. Algebraic!

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

44. Algebraic!

what are they??

45. lovekblue

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

46. Algebraic!

what functions bound the region in the last picture?

47. Algebraic!

hint: I already did it for you.

48. lovekblue

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

49. Algebraic!

trace the boundary

50. Algebraic!

|dw:1352778560923:dw|

51. Algebraic!

what's that portion?

52. Algebraic!

say "y=0"

53. Algebraic!

|dw:1352778627593:dw|

54. Algebraic!

what's that portion?

55. lovekblue

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

56. lovekblue

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

57. Algebraic!

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

58. Algebraic!

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

59. lovekblue

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

60. Algebraic!

trace the boundary of each region

61. Algebraic!

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

62. lovekblue

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

63. Algebraic!

yes

64. lovekblue

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

65. Algebraic!

not necessarily..

66. Algebraic!

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

67. Algebraic!

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

68. lovekblue

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

69. lovekblue

ya, i do get that part

70. Algebraic!

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71. lovekblue

is that region not what the last picture look like?

72. Algebraic!

for the second part... yep.

73. lovekblue

can i ask what does "region " mean..

74. Algebraic!

the red areas in the first part.

75. lovekblue

yea..what does that red area mean

76. lovekblue

is it like the path of rotation or something?

77. Algebraic!

no.

78. Algebraic!

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

79. Algebraic!

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80. Algebraic!

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

81. Algebraic!

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

82. lovekblue

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

83. Algebraic!

|dw:1352779702320:dw|

84. Algebraic!

yes, exactly.

85. lovekblue

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

86. lovekblue

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

87. Algebraic!

the second multiple choice question? or a new question?

88. lovekblue

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

89. lovekblue

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

90. Algebraic!

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

91. Algebraic!

inner radius is 5, outer radius is 10 - 5e^-x

92. Algebraic!

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

93. lovekblue

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

94. Algebraic!

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

95. Algebraic!

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

96. Algebraic!

that should be pretty easy to integrate...

97. lovekblue

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

98. lovekblue

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

99. lovekblue

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