A) zero
B) \[{{x}_{2}}^{2}-{{x}_{1}}^{2}\]
C) \[2{{x}_{2}}({{x}_{2}}-{{x}_{1}})\]
D) \[2{{x}_{1}}({{x}_{1}}-{{x}_{2}})\]
Correct Answer: B
Solution :
Mechanical work (W) is the force applied through a distance, defined mathematically as the line integral of a scalar product of force (F) and displacement (dx) vectors. \[W=\int{Fdx}\] Given, \[F=2x,\] Using \[\int{{{x}^{n}}dx}=\frac{{{x}^{n+1}}}{n+1}\] \[\therefore \] \[W=\int_{{{x}_{1}}}^{{{x}_{2}}}{2x\,\,dx=2\left[ \frac{{{x}^{2}}}{2} \right]_{{{x}_{1}}}^{{{x}_{2}}}}\] \[=({{x}_{2}}^{2}-{{x}_{1}}^{2})\]
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