R is the region bounded by the functions f(x)=3x2+27x+54 and g(x)=−3x22−27x2−27. Find the area A of R. Enter an exact answer.

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{:[f(x)=3x^(2)+27 x+54;quad g(x)=-(3x^(2))/(2)-(27 x)/(2)-27.],[A=int_(a)^(b)|f(x)-g(x)|dx.],[3x^(2)+27 x+54=-(3)/(2)x^(2)-(27)/(2)x-27.],[6x^(2)+81 x+162=-3x^(2).],[9x^(2)+81 x+162=0.],[(x+3)(x+6)=0],[R=int_(-6)^(-3)|3x^( ... See the full answer