How to find volume of a curve [f(x)] which is rotated along y-axis?

We have a input function y = f(x) and we have to find the volume along x-axis and y-axis. (solid of revolution) The minimum and maximum values of x are given

I am getting the volume along x-axis but I am getting an error while finding the volume along the y-axis.

The values of f(x) and domain is : -

1. x^(1/2), 0<=x<=4
2. 3*cos(0.4*x+pi), -5<=x<=5
3. sin(x)+3, -5<=x<=5
4. x^3, 0<=x<=3

Here is my code

%Volume along x-axis
clc
clear all

syms x y

%fx = input('Enter the function : ')


xmin = input('Enter minimum value of x : ')
xmax = input('Enter maximum value of x : ')

intfx = int((fx)^2,xmin,xmax)

vx = pi*(intfx)
vx = double(vx)
sprintf('The volume along x-axis is %d',vx)








%Volume along y-axis
y_fx_equation_wrt_x = y == fx
x_fy_equation_wrt_y = solve(y_fx_equation_wrt_x, x)
fy = x_fy_equation_wrt_y

ymin = subs(fx,x,xmin)
ymax = subs(fx,x,xmax)


intfy = abs(int(fy^2,ymin,ymax))
vy = pi*(intfy)
vyy = double(vy)


sprintf('The volume along y-axis is %d',vyy)

In output 1 I get an error but on output 2 I don't.

What am I doing wrong?

Output 1

y = 3*cos(0.4*x+pi)

3*cos(0.4*x+pi)

fx =

-3*cos((2*x)/5)

Enter minimum value of x :

-5

xmin =

-5

Enter maximum value of x :

5

xmax =

5

intfx =

(45*sin(4))/4 + 45

vx =

pi*((45*sin(4))/4 + 45)

vx =

114.6241

ans =

'The volume along x-axis is 1.146241e+02'

y_fx_equation_wrt_x =

y == -3*cos((2*x)/5)

x_fy_equation_wrt_y =

(5*pi)/2 - (5*acos(y/3))/2

(5*pi)/2 + (5*acos(y/3))/2

fy =

(5*pi)/2 - (5*acos(y/3))/2

(5*pi)/2 + (5*acos(y/3))/2

ymin =

-3*cos(2)

ymax =

-3*cos(2)

Error using ^ (line 442)

Matrix must be square.

Error in Week6classwork1_2 (line 35)

intfy = abs(int(fy^2,ymin,ymax))

Output 2

y = x^(0.5)

Enter the function :

x^(0.5)

fx =

x^(1/2)

Enter minimum value of x :

0

xmin =

0

Enter maximum value of x :

4

xmax =

4

intfx =

8

vx =

8*pi

vx =

25.1327

ans =

'The volume along x-axis is 2.513274e+01'

y_fx_equation_wrt_x =

y == x^(1/2)

Warning: Solutions are only valid under certain conditions. To include parameters and conditions in the solution, specify the 'ReturnConditions' value as 'true'.

x_fy_equation_wrt_y =

y^2

fy =

y^2

ymin =

0

ymax =

2

intfy =

32/5

vy =

(32*pi)/5

vyy =

20.1062

ans =

'The volume along y-axis is 2.010619e+01'