Given functions

Question

f(x)=-x²+4 and g(x)=-x³+4x for -2<=x<=1.

a.    Make a graph of the functions.

Compute the centroid.

b.    Compute M.

c.    Compute M_y.

d.    Compute x_c (the x centroid)

e.    Compute M_x.

f.     Compute y_c (the y centroid)

g.    Plot the centroid on your graph.

h.    Does your computed centroid look like it at the center of mass of your graph? (yes or no)

Answer 1

Graph these functions!

The center of mass in the x direction is given by∫

∫ x[x²+4-(x³+4x)] dx divided by the area of the figure,

Limits of integration -2 and 1.

The center of mass in the y direction is similar but requires 2 integrals in the numerator and you will need to figure the limits out.

The integrations are not difficult but messy.

If you have specific questions, please comment so that I can try to help.