Find area of region bounded by x^3 - 6x and -2x

[Tskate]

Find the area of the region bounded by the graphs of f(x)= x^3-6x and g(x)= -2x Prove if it has symmetry

I know it intersects at (-2,4), (0,0), & (2,-4)

 

[o_O]

Re: Find the area of the region

Well your area can be found by splitting it into two definite integrals and adding the two up since:
\(\displaystyle g(x) > f(x) \:\: \mbox{for}\:\: x \in (-2, 0)\:\: \mbox{and}\:\:f(x) > g(x)\:\: \mbox{for}\:\:x \in (0,2)\)

\(\displaystyle \mbox{Area} \: = \int_{-2}^{0} (g(x) - f(x)) + \int_{0}^{2} (f(x) - g(x))\)

And to prove if it is symmetrical, use the definition of an even or odd function and see if it satisfies one of them:
\(\displaystyle \mbox{Even} \: : f(x) = f(-x)\)
\(\displaystyle \mbox{Odd} \: : f(-x) = -f(x)\)