We want to find the area of the region of the plane bounded by the curves y=x^3 and y=9x .

a): Find the three points of intersection of these two curves: (x1,y1) , (x2,y2) and (x3,y3) with x1

x1= y1= x2= y2= x3= y3=

b): By drawing the graph of this region, we find that the area of the region bounded by the two curves is given by the integral ba|x^39x|dx with a

a= and b=

c): To evaluate the integral in (b), we must divide the domain of integration in two. We have

ba|x^39x|dx=caf1(x)dx+bcf2(x)dx with a

c=

f1(x)=

and

f2(x)=

d): Evaluate the integrals in (c) to find the area of the region bounded by the two curves above.

ba|x^39x|dx=