whats logic behind calculating volume of region in a graph by integration?
you just take it with respect to x,find out limit points,and integrate the term which is equal to y^2?

Question

whats logic behind calculating volume of region in a graph by integration?
you just take it with respect to x,find out limit points,and integrate the term which is equal to y^2?

anonymous · Answer

@electrokid

anonymous · Answer

in calculus, everything is represented by an infinitesimally small element.

to find volume, you create a small dV (as a small hight cylinder->disc method, small diameter cylinder->shell method, etc.)
then you sum up all the possible number of those elements.

anonymous · Answer

so what about in graphs
like if you got equations

anonymous · Answer

what about that?

anonymous · Answer

like to find volume of rotating ellipsoid

anonymous · Answer

yes, rotation will create the boundaries of the shape. How else can there be a 3D element? 
also, the rotation makes life simpler coz, it gives you a symmetric figure and you can get away with a single integral. It is a common practice to use triple integrals to find the volumes and double integrals to find the areas.
Thats why we perform transformations of co-ordinate systems -> they provide you a different view of the same thing.

anonymous · Answer

so you just integrate y value right?
$$\pi \int\limits_{a}^{b}y^2dx ???$$

anonymous · Answer

is it applicable to all?

anonymous · Answer

so, volume = area of base * height
your disc is vertical with radius "y", and height is "dx"

So, I assume the curve is rotated about x-axis

anonymous · Answer

yeah