For the following exercises, use the method of shells to approximate the volumes of some common objects, which are pictured in accompanying figures. 160. Use the method of shells to find the volume of an ellipse ( x 2 / a 2 ) + ( y 2 / b 2 ) = 1 rotated around the x-axis.
For the following exercises, use the method of shells to approximate the volumes of some common objects, which are pictured in accompanying figures. 160. Use the method of shells to find the volume of an ellipse ( x 2 / a 2 ) + ( y 2 / b 2 ) = 1 rotated around the x-axis.
Rotate the ellipse
x2
a2
+
y2
b2
= 1
around the x-axis to approximate the volume (in units3) of a footbal
Complete the following problems.
a. Express the area A of the cross-section cut from the ellipsoid
b. Use slices perpendicular to the z-axis to find the volume V of the ellipsoid in part (a).
22
3² 3² 2²
c. Now find the volume of the ellipsoid- 2
abc
=1 by the plane z= d as a function of d. (The area of an ellipse with semiaxes a and b is rab.)
4 25
1. Does your formula give the volume of a sphere of radius a if a = b=c?
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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