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Integrations Volume Question Need Help! :( (1 Viewer)

kevinsta

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Find the volume of the solid of
revolution formed if the area
enclosed between the curves
y=x^2 and y=(x-2)^2 is rotated
about the x-axis.
 

FrankXie

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there is no region bounded by these two parabolas, the correct way to refer the area is "enclosede by parabolas ... and ... and the x axis"
the solution is easy, split the region into two parts: 0 to 1, and 1 to 2. integrate respectively and add up.
 

kevinsta

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there is no region bounded by these two parabolas, the correct way to refer the area is "enclosede by parabolas ... and ... and the x axis"
the solution is easy, split the region into two parts: 0 to 1, and 1 to 2. integrate respectively and add up.
I keep getting the wrong answer tho. My algebra is clearly wrong can you perhaps show me?
 

Silly Sausage

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Recall
You can integrate separately for the corresponding areas by letting:


 
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kevinsta

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oh yeah remember how for volume it's pi outside so times the ans by pi
but why only 2 pi/3 lol?
My friend did it he basically just integrated y^2=x^4 and multiplied it by 2.... which makes sense when you draw the graph but like... :(
 
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My friend did it he basically just integrated y^2=x^4 and multiplied it by 2.... which makes sense when you draw the graph but like... :(
ahhh symmetrical, which is funny because I actually posted the diagram. Dammit, but wouldn't there be more than just that method?
ok that's solved
 

kevinsta

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ahhh symmetrical, which is funny because I actually posted the diagram. Dammit, but wouldn't there be more than just that method?
ok that's solved
Yea I know I want to learn the algebraically method that always works, because usually they aren't symmetrical and I don't want to repeat the same mistake.
 

kevinsta

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most of the time I sketch but omg when I do a mistake in the diagram, I'm doomed
LOOOOOOOOOOOOOOOOOL I hate drawing graphs TBH I suck at drawing :( Teacher tells me off when I don't draw graphs and im like IT DON'T TELL ME TO DRAW GRAPHS PLEASE... haven't met alot of people that actually use the word "doomed" like myself
 
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LOOOOOOOOOOOOOOOOOL I hate drawing graphs TBH I suck at drawing :( Teacher tells me off when I don't draw graphs and im like IT DON'T TELL ME TO DRAW GRAPHS PLEASE... haven't met alot of people that actually use the word "doomed" like myself
Yes, doomed is a word used when I exaggerate a lot. My teacher likes a sketch no matter how messy because he can't draw too. Btw, you doing hsc this year?
 
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