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what's your question?

ah I see those are multiple choices...

did you get the 'sketch the region' one?

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

you there?

yes i am here..

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

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

(and x=4)

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

for my function, x is not 0 u mean?

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

what lines do you trace for the last choice?

|dw:1352777609189:dw|

|dw:1352777630991:dw|

|dw:1352777716676:dw|

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

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

yes

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

it does mention y=5 however...

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

naw..

then u can kinda know there is a hole in between

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

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

i still think is the last one..

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

why is it the last one..

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

first part ..

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

ok..

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

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

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

what are they??

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

what functions bound the region in the last picture?

hint: I already did it for you.

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

trace the boundary

|dw:1352778560923:dw|

what's that portion?

say "y=0"

|dw:1352778627593:dw|

what's that portion?

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

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

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

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

i'm not sure what u mean by bounded..do you mean by starting from thereï¼Ÿ

trace the boundary of each region

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

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

yes

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

not necessarily..

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

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

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

ya, i do get that part

|dw:1352779152955:dw|

is that region not what the last picture look like?

for the second part... yep.

can i ask what does "region " mean..

the red areas in the first part.

yea..what does that red area mean

is it like the path of rotation or something?

no.

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

|dw:1352779636199:dw|

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

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

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

|dw:1352779702320:dw|

yes, exactly.

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

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

the second multiple choice question? or a new question?

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

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

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

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

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

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

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

that should be pretty easy to integrate...

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

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

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