SOLUTION: Find the area of the region bounded by functions:
{{{ f(x)= -x^2 + 3x }}} and {{{ g(x) = 2x^3 - x^2 - 5x }}}
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-> SOLUTION: Find the area of the region bounded by functions:
{{{ f(x)= -x^2 + 3x }}} and {{{ g(x) = 2x^3 - x^2 - 5x }}}
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Three solutions (points of intersection):
x=0; x-2=0; x+2=0
x=2; x=-2
The curves intersect at (-2,-10), (0,0), (2,2)
As we see, there are two loops bound by these curves.
We must find the areas of the two loops separately, because
the upper curve in the left loop is the lower curve in the
loop on the right.
Left loop:
Right loop:
Total area = 8+8 = 16
Edwin
