Answer
$$0$$
Work Step by Step
$$W=\int ^{4}_{1}f_{1}\left( x\right) dx+\int ^{1}_{4}f_{2}\left( x\right) dx=\int ^{4}_{1}3x^{2}dx+\int ^{1}_{4}3x^{2}dx=x^{3}]^{4}_{1}+x^{3}]^{1}_{4}=\left( 4^{3}-1^{3}\right) +\left( 1^{3}-4^{3}\right) =0$$
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