Answer
$\dfrac{k(b-a)}{ab}$
Work Step by Step
Hooke's Law states that $F=k x$
Use formula: $\int x^n=\dfrac{x^{n+1}}{n+1}+C$
This implies that
$W=\int_b^{a} (\dfrac{-k}{x^2}) dx$
Use formula: $\int x^n=\dfrac{x^{n+1}}{n+1}+C$
Then $W=k[(x^{-1}]_b^{a}=k[(\dfrac{1}{x})]_b^{a}$
Hence, $W=(k)[\dfrac{1}{a}-\dfrac{1}{b}]=\dfrac{k(b-a)}{ab}$
