Answer
$16$
Work Step by Step
Given the values in question
$\int ^{4}_{2}x^3dx=60;$
$\int ^{4}_{2}xdx=6;$
$\int ^{4}_{2}dx=2$
$$\Rightarrow \int ^{4}_{2}\left( \dfrac {1}{2}x^{3}-3x+2\right) dx=\int ^{4}_{2}\dfrac {1}{2}x^{3}dx-\int ^{4}_{2}3xdx+\int ^{4}_{2}2dx=\dfrac {1}{2}\int ^{4}_{2}x^{3}dx-3\int ^{4}_{2}xdx+2\int ^{4}_{2}dx=\dfrac {1}{2}\times 60-3\times 6+2\times 2=16 $$
