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For questions about problems related to physics that involve evaluating integrals. Purely mathematical questions should be asked at math.SE.
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Find the work done against the force
If there is a force $\mathbf F(x)=ax\hat i$ and an object is moving from $x_2>0$ to $x_1>0$ in the opposite direction of force. Then work could be calculated as follows
$$\int_{x_2}^{x_1} -F(x)\cdot\ …