Question

The work done by an applied variable force $F=x+x^3$ from $x=om$ to $x=2,m$ where $x$ is displacement, is

• A. 6J
• B. 8J
• C. 10J
• D. 12J

Answer 1

Answer: (A)

Given $F=x+x^3$
and $x=0m$ to $x=2m$
We know
$W=\int Fdx$
$W=\underset{0}{\overset{2}{\int }}\left(x+x^3\right)dx$
$W={\left[\frac{x^2}{x^4}4\right]}_0^2$
$W=\left[\frac{4}{2}+\frac{16}{4}\right]$
$W=6J$