Answer:
The answer is "Option C."
Step-by-step explanation:
[tex]y=6x, \ \ y=x, \ \ , y=24,\\[/tex]
In this we calculate two points that are (0,4) and(4,24)
on[0,4]
shell radius=x
height = 6x-x
=5x
on[4,24]
shell radius=x
height = 24x-x
6x=24
x=4
Calculating shell volume by shell method:
[tex]v=\int\limits^b_a {2\pi(radius) \cdot(height)} \, dx \\[/tex]
[tex]=\int\limits^4_0 {2\pi(x) \cdot(5x)} \, dx +\int\limits^{24}_4 {2\pi(x) \cdot(24-x)} \, dx \\\\=\int\limits^4_0 {10\pi(x^2) dx +\int\limits^{24}_4 {2\pi x(24-x)} \, dx[/tex]
That's why the answer is "Option C".
