Prove the following two theorems of Pappus: Let a curve y = f x be revolved about the x axis, thus forming a surface of revolution. Show that the cross sections of this surface in any plane x = const. [that is, parallel to the y , z plane] are circles of radius f x . Thus write the general equation of a surface of revolution and verify the special case f x = x 2 in (3.9).
Prove the following two theorems of Pappus: Let a curve y = f x be revolved about the x axis, thus forming a surface of revolution. Show that the cross sections of this surface in any plane x = const. [that is, parallel to the y , z plane] are circles of radius f x . Thus write the general equation of a surface of revolution and verify the special case f x = x 2 in (3.9).
Let a curve
y
=
f
x
be revolved about the x axis, thus forming a surface of revolution. Show that the cross sections of this surface in any plane
x
=
const. [that is, parallel to the
y
,
z
plane] are circles of radius
f
x
.
Thus write the general equation of a surface of revolution and verify the special case
f
x
=
x
2
in (3.9).
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY