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

[kevinsta]

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]

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]

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?

 

[snowflakeptical]

^ oh yeah like this

I'll try that as well

 

[snowflakeptical]

I got 33/5 units^3
did anyone else?

 

[Silly Sausage]

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

 

[kevinsta]

I got 33/5 units^3
did anyone else?

YES I GOT THAT TOOO But the answer says 2PI/3 units^3

and I got 33Pi/5 Units^3

 

[kevinsta]

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

Don't you have to combine the equations together??

 

[snowflakeptical]

YES I GOT THAT TOOO But the answer says 2PI/3 units^3

and I got 33Pi/5 Units^3

oh yeah remember how for volume it's pi outside so times the ans by pi
but why only 2 pi/3 lol?

 

[kevinsta]

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...

 

[snowflakeptical]

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]

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.

 

[snowflakeptical]

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.

most of the time I sketch but omg when I do a mistake in the diagram, I'm doomed

 

[kevinsta]

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

 

[snowflakeptical]

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?