Use the shell
method to ﬁnd the volume of the solid generated by revolving 
about the y-axis.

x=sqrt(9-x^2) and x=0

Question

Use the shell
method to ﬁnd the volume of the solid generated by revolving 
about the y-axis.

x=sqrt(9-x^2) and x=0

callisto · Answer

The equation should be$$y =\sqrt{9-x^2}$$?

callisto · Answer

Assume the equation of the line is $y=\sqrt{9-x^2}$
Domain of the function: [-3, 3]
So, integrate from x=0 to x=3

$$V=\int_0^3 2\pi xf(x) dx = 2\pi \int_0^3 x\sqrt{9-x^2} dx=...$$

raden · Answer

if revolving  about the y-axis, the integration should forward dy
so, v=pi*int((f(y))^2 dy [y1,y2]
with y1 and y2 are under interval and up interval respectively

callisto · Answer

Shell method.... about y-axis => dx See this: http://mathworld.wolfram.com/MethodofShells.html

callisto · Answer

@RadEn Yours is disc method, I think

raden · Answer

yea, sorry i knew just new about the sell methode, @Callisto... sorry again :)

callisto · Answer

It's okay, don't worry :)