what is the volume of the solid, spun around the y axis of f(x) = 2x^2 -x^3, from x=[0,2] ?

Question

amistre64 · Answer

in other words, bounded by f(x) and the positive x axis

anonymous · Answer

The integration Of the function squared. Only difference is, you solve for x in terms of y.

amistre64 · Answer

thats a bit difficult; lots of radicals involved; there is an easier way tho :)

anonymous · Answer

Yeah, there are 2 schools of thought, sorta. One is rings vs cylinders. The other is discs/shells/washers.

anonymous · Answer

I usually prefer the rings, but with a quadratic, yeah it is more annoying.

amistre64 · Answer

yep; shells is your best bet

take an average cylinder of height f(x) and cut it straight up and flatten it out so that it is 2pi x wide

anonymous · Answer

Yeah, that'd do it. Haha

amistre64 · Answer

total area of the flattened cylinder is 2pi x [f(x)]

2pi [S] x[f(x)] dx in the interval gives you the volume :)

amistre64 · Answer

trying to do it the other way; nightmare integral lol

anonymous · Answer

That's the beauty of choices though haha. Why did you ask a question you know the answer to?

amistre64 · Answer

to see if anyone could answer it of course ;)

amistre64 · Answer

i cant keep all the medals :)

anonymous · Answer

Very fair. I'm up to my eeballs in calculus. But Haha that's just cuz I haven't been here in a bit. ;)

anonymous · Answer

I just started a few days ago orso.

amistre64 · Answer

im taking it over the summer; calc1 that is

anonymous · Answer

Oh cool. I just took the test to get credit through Calc 2.

amistre64 · Answer

i was gonna to save time, but cant make it 50 miles to the official testing cite .....

amistre64 · Answer

so i take the classes and do my crosswords and pass

anonymous · Answer

Haha I play solitaire.

anonymous · Answer

There, I posted one for y