Let R be the shaded region bounded by the graph of $y = xe^x$, the line $y = -2x$,
and the vertical line $x = 1$, as shown in the figure above.
(a) Find the area of R.
(b) Write, but do not evaluate, an integral expression that gives the volume of the
solid generated when R is rotated about the horizontal line $y = -2$.
(c) Write, but do not evaluate, an expression involving one or more integrals that
gives the perimeter of R.
(d) Write, but do not evaluate an integral expression for the volume of the solid where the hypotenuse
of an isosceles right triangle is embedded in region R and are perpendicular to the x-axis.
