lovekblue
Need help in integral area involve 3d objects



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lovekblue
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Algebraic!
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what's your question?

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ah I see those are multiple choices...

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did you get the 'sketch the region' one?

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

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you there?

Algebraic!
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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...

lovekblue
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yes i am here..

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

lovekblue
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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 ?

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

Algebraic!
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(and x=4)

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

lovekblue
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for my function, x is not 0 u mean?

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

Algebraic!
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what lines do you trace for the last choice?

Algebraic!
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dw:1352777609189:dw

lovekblue
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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?

Algebraic!
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dw:1352777630991:dw

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dw:1352777716676:dw

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

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

lovekblue
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yes

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

Algebraic!
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it does mention y=5 however...

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

Algebraic!
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naw..

lovekblue
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then u can kinda know there is a hole in between

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

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

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

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

lovekblue
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i still think is the last one..

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

Algebraic!
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why is it the last one..

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

lovekblue
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first part ..

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

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ok..

lovekblue
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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

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

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

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

Algebraic!
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what are they??

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

Algebraic!
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what functions bound the region in the last picture?

Algebraic!
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hint: I already did it for you.

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

Algebraic!
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trace the boundary

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dw:1352778560923:dw

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what's that portion?

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say "y=0"

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dw:1352778627593:dw

Algebraic!
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what's that portion?

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

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

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

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

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

Algebraic!
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trace the boundary of each region

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

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

Algebraic!
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yes

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

Algebraic!
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not necessarily..

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

Algebraic!
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so the inner radius is 5 and the outer radius is 105e^x

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

lovekblue
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ya, i do get that part

Algebraic!
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dw:1352779152955:dw

lovekblue
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is that region not what the last picture look like?

Algebraic!
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for the second part... yep.

lovekblue
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can i ask what does "region " mean..

Algebraic!
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the red areas in the first part.

lovekblue
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yea..what does that red area mean

lovekblue
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is it like the path of rotation or something?

Algebraic!
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no.

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

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dw:1352779636199:dw

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

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

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

Algebraic!
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dw:1352779702320:dw

Algebraic!
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yes, exactly.

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

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

Algebraic!
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the second multiple choice question? or a new question?

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

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

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

Algebraic!
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inner radius is 5, outer radius is 10  5e^x

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

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

Algebraic!
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\[\pi \int\limits_{ }^{} (105e^{x})^2  5^2 dx\]

Algebraic!
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\[\pi \int\limits_{0}^{4} 75 100e^{x} +25e^{2x} dx\]

Algebraic!
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that should be pretty easy to integrate...

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

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

lovekblue
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i got pi ((300+10 e^4  25/2 e^8) (1025/2))