Question

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

• A. $2$ units
• B. $4$ units
• C. $6$ units
• D. $8$ units

Answer 1

Answer: (B)

$4$ units

Answer 2

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