Question

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

• A. 6J
• B. 8J
• C. 10J
• D. 12J

Answer 1

Answer: (A)

6J

Answer 2

Given $F = x +x^{3}$
and $x =0 m$ to $x =2 m$
We know
$W=\int F d x$
$W =\int\limits_{0}^{2}\left(x +x^{3}\right) d x$
$W=\left[\frac{x^{2}}{x^{4}} 4\right]_{0}^{2}$
$W=\left[\frac{4}{2}+\frac{16}{4}\right]$
$W=6\, J$