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    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 helpsmiley
 

 Apr 29, 2020
 #1
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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.

 

 Apr 29, 2020

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