First, find where the graphs intersect:
x^3+3x = 5x^2-x
x^3 - 5x^2 + 4x = 0
x(x-4)(x-1) = 0
Now, f(x) > g(x) from 0 to 1
g(x) > f(x) from 1 to 4
If you want geometric area, break the integration into two intervals. If you want algebraic (signed) area, then just integrate from 0 to 4.
The actual integration is just powers, so it's simple.
Let f(x)=x^3+3x and g(x=5x^2-x
Determine the area of the region enclosed by the graphs of f and g.
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