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(B) The work done $W$ by a variable force $F$ is given by the integral of the force with respect to displacement:$W = \int_{0}^{x_1} F \cdot dx$Substi

Vedclass · Accepted Answer

$\frac{1}{2}Cx_1^2$

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(B) The work done $W$ by a variable force $F$ is given by the integral of the force with respect to displacement:$W = \int_{0}^{x_1} F \cdot dx$Substitute the given force $F = Cx$ into the integral:$W = \int_{0}^{x_1} Cx \, dx$Since $C$ is a constant,we can take it out of the integral:$W = C \int_{0}^{x_1} x \, dx$Using the power rule for integration $\int x^n dx = \frac{x^{n+1}}{n+1}$:$W = C \left[ \frac{x^2}{2} \right]_{0}^{x_1}$Evaluating the definite integral:$W = C \left( \frac{x_1^2}{2} - \frac{0^2}{2} \right) = \frac{1}{2}Cx_1^2$

$A$ particle moves under the effect of a force $F = Cx$ from $x = 0$ to $x = x_1$. The work done in the process is

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