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  4. A force F = 3x2 + 2x + 1 acts on a body in the x -direction. The work done by this force during a displacement from x = -1 to +1 is

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Q. A force $ F = 3x^2 + 2x + 1 $ acts on a body in the $ x $ -direction. The work done by this force during a displacement from $ x = -1 $ to $ +1 $ is

J & K CETJ & K CET 2019

Solution:

$F=3x^{2}+2x+1$
$W=\int\limits_{-1}^{1}Fdx =\int\limits_{-1}^{1} \left(3x^{2}+2x+1\right)dx$
$=\left[x^{3}+x^{2}+x\right]_{-1}^{1}$
$\Rightarrow 3+1$
$4$ units