Volumes of Revolution

The region bounded by the graph of $f(x)=x^2$, the $Ox$ axis, and the line $x=2$ (for $x\in [0,2]$) is rotated about the $Oy$ axis. Using the shell method ($V=2\pi {\displaystyle {\int }_0^{2}xf(x)dx}$), the volume of the resulting solid is:

The volume generated by rotating $f(x)=x$ on $[0,3]$ about the $x$-axis is:

The volume generated by rotating $f(x)=2$ on $[0,5]$ about the $x$-axis is:

The volume of the solid generated by rotating $f(x)\ge 0$ on $[a,b]$ about the $x$-axis is:

The volume generated by rotating $f(x)=\cos x$ on $[0,\pi \mathrm{/}2]$ about the $x$-axis is closest to:

The volume generated by rotating $f(x)=e^x$ on $[0,1]$ about the $x$-axis is:

The volume generated by rotating $f(x)=\sqrt{x}$ on $[0,4]$ about the $x$-axis is:

The volume generated by rotating $f(x)=x^2$ on $[0,1]$ about the $x$-axis is:

Rotating $f(x)=\sqrt{R^2-x^2}$ on $[-R,R]$ about the $x$-axis generates a:

The volume of the solid generated by rotating the region between $y=x$ and $y=x^2$ on $[0,1]$ about the $x$-axis equals: