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volumes of cross sections

yes that is it ! thank you !

that's also the formula used in solids formed by revolution of some curve about some axis

you know where we take circles as the cross section

no A(x) is the area
you don't want to square the area

o ok

if the cross section is a circle then A(x)=pi*r^2

where r is a function of x

though we could look at things in terms of y too
not just x

you know depending on what suits us better

i think the f(x) is actually the radius

f(x) is the function

i mean the height of the funtion

yes which is intern the radius
so A=pi*r^2

and freckles just use the Area instead...i think

I guess i am kind of confuse lol

what's the question?

area of a circle is what I called A(x)

or the are of the cross section is A(x)

|dw:1440894543729:dw|
Say we want to take this curve on [a,b] and rotate it about the x-axis

|dw:1440894662165:dw|
so we have a cross section that is a circle

\[\int\limits_{a}^{b}A(x) dx \\ \text{ so we have } A(x)=\pi \cdot (f(x))^2 \\ \]

so i was right about f(x) being the radius?

ohh i see

|dw:1440894830121:dw|
yes

but the A(x) is not squared

A(x) just means area of the cross section

ohh i see ! I thought f(x) was just the height of the function

It makes so much sense now :)

well you can also say |f(x)| is the height of the function

cool..