Answer:
Option b
Step-by-step explanation:
given that a region is bounded by the curves [tex]y = x^2 \\y = 2[/tex]
It is rotated about x axis
We are to use shell method
Region picture is enclosed
We are to use shell method
Due to symmetry we can find form 0 to 2 and double it.
Here limits for y are from 0 to 2
The variable x can be written as
[tex]x=\sqrt{y}[/tex]
A(y) = area = [tex]2\pi (radius)(width)\\= 2\pi (y) (\sqrt{y} )[/tex]
Volume = [tex]2\int\limits^2_0 {2\pi y\sqrt{y} } \, dy\\=4\pi\int\limits^2_0 y^{\frac{3}{2} } dy[/tex]
Hence option b is right
volume of the solid
