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Q.
A force $F=A y^{2}+B y+C$ acts on a body in the $y$ -direction. The work done by this force during a displacement from $y=-a$ to $y=a$ is
Work, Energy and Power
Solution:
$ W=\int F d y=\int\limits_{-a}^{+a}\left(A y^{2}+B y+C\right) d y $
$\left[\frac{A y^{3}}{3}+\frac{B y^{2}}{2}+C y\right]_{-a}^{+a} $
$=\left[\frac{A a^{3}}{3}+\frac{B a^{2}}{2}+C a\right]-\left[-\frac{A a^{3}}{3}+\frac{B a^{2}}{2}-C a\right] $
$=\frac{2 A a^{3}}{3}+2 C a$