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Sagot :
Integrate the force function over the given displacement:
[tex]W = \displaystyle \int_{x=0.00\,\rm m}^{x=2.00\,\rm m} \left(3.00\frac{\rm N}{\mathrm m^2}\right) x^2 + \left(2.00\frac{\rm N}{\rm m}\right) x \, dx[/tex]
[tex]W = \displaystyle \left(1.00\frac{\rm N}{\mathrm m^2}\right) x^3 + \left(1.00\frac{\rm N}{\rm m}\right) x^2 \bigg|_{x=0.00\,\rm m}^{x=2.00\,\rm m}[/tex]
[tex]W = \displaystyle \left(1.00\frac{\rm N}{\mathrm m^2}\right) (2.00\,\mathrm m)^3 + \left(1.00\frac{\rm N}{\rm m}\right) (2.00\,\mathrm m)^2[/tex]
[tex]W = \displaystyle 8.00 \, \mathrm N{\cdot}\mathrm m + 4.00 \,\mathrm N{\cdot}\mathrm m = \boxed{12.0 \, \mathrm J}[/tex]
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