1. The shaded regions R1 and R2, shown below, are enclosed by the graphs of
f(x)=x^3-6x,g(x)=e^(-x).
a. Find the x- and y-coordinates of the three points of intersection of the graphs of f and g. Please show the equation you would solve to find these (and then use Geogebra or a graphing calculator).
b. Find the area of R1.
c. Find the area of R2.
d. Find the exact volume of the solid formed by revolving R1 about the x-axis.
Thank you for the help
+33616 It's useful to draw the following graph (I'll leave you to do it in Geogebra or a graphing calculator). I've found the roots using a Newton-Raphson numerical method, but the question suggests you might be expected to find them simply by picking them off your graph.
For parts b, c and d I've indicated how it's done, but I'll leave you to do the integrations.
