Question

Solve using MATLAB. Use the method of cylindrical shells to find the volume generated by rotating the region bounded by y=4-2x, y=0, x=0 about x=-1.

Answer 1

step 1:

The method of cylindrical Shells. says that, Volume = upper bound 211. (Shell radius). (Shell height). de lower bound Here the given region the lwave is, bounded by y=4-22, y = 0, a=0 y = 4-27 of, 2x +y = 4 --) 4 2 2 ty 4 ل 3 94-22 + Shell height 1 1 - 1 2 2 } Shell radino volumer generated by rotating about 25-1 211: (2+1). (4-22).dą Now, we are going to use matlab to solve this. Sa 0

Matlab code for the integration part:

clear all

syms x

expr=2*pi*(x+1)*(4-2*x);

F=int(expr,[0,2])

output:

F =

(40*pi)/3

screenshot:

>> clear all >> syms x >> expr=2*pi*(x+1)*(4-2*x); >> F=int(expr, [0,2]) F = (40*pi)/3

Summary:

Here the function is stored in expr

int() is a matlab function for integration of a certain function .If we have to find the integration for a particular range then we have to pass it as parameter as I have done here.

So,the volume generated by rotating the region about x=-1 is 40*pi/3.