(Solved): 4. a) Find the volume of the solid of revolution generated by revolving the region between \( y=e^ ...

4. a) Find the volume of the solid of revolution generated by revolving the region between \( y=e^{x}, y=0, x=0 \), and \( x=2 \), around the axis \( x=-1 \). b) Find the volume of the solid whose base is the region bounded between the curves \( y=\sqrt{x} \) and \( y=\frac{1}{\sqrt{x}} \) for \( 1 \leq x \leq 4 \) and whose cross sections perpendicular to the \( x \)-axis are squares. Set up, but DO NOT evaluate the integral.