Applications of definite integral

The function $f(x)=x^2+2$ is graphed in the picture. Consider the region between the graph of the function on the interval $[0;1]$, both axes and the line $x=1$. Find the formula for the volume of the solid of revolution obtained by revolving this region about $y$-axis.

The function $f(x)=\sqrt{x}$ is graphed in the picture. Consider the region bounded by the graph of $f$ on $[1;4]$, lines $x=1$, $x=4$ and the $x$-axis. Identify the formula for volume of the solid of revolution obtained by revolving this region about the $x$-axis.

The function $f(x)=1$ is graphed in the picture. Determine the solid of revolution with volume given by the following formula. $$\pi {\int }_{-1}^1{f}^2(x)\mathrm{d}x$$

The function $f(x)=3-2x$ is graphed in the picture. Consider the region between the graph of the function $f$, the $x$-axis and the lines $x=1$ and $x=-1$. Find the volume of the solid of revolution obtained by revolving this region about $x$-axis.