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

Guest Apr 29, 2020

#1**+4 **

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.

Alan Apr 29, 2020