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Q.
The work done by an applied variable force $F=x +x^{3}$ from $x=o m$ to $x=2, m$ where $x$ is displacement, is
Delhi UMET/DPMTDelhi UMET/DPMT 2011Work, Energy and Power
Solution:
Given $F = x +x^{3}$
and $x =0 m$ to $x =2 m$
We know
$W=\int F d x$
$W =\int\limits_{0}^{2}\left(x +x^{3}\right) d x$
$W=\left[\frac{x^{2}}{x^{4}} 4\right]_{0}^{2}$
$W=\left[\frac{4}{2}+\frac{16}{4}\right]$
$W=6\, J$