  We study the swelling of a flexible linear chain composed of active particles
by analytical theory and computer simulation. Three different situations are
considered: a free chain, a chain confined to an external harmonic trap, and a
chain dragged at one end. First we consider an ideal chain with harmonic
springs and no excluded volume between the monomers. The Rouse model of
polymers is generalized to the case of self-propelled monomers and solved
analytically. The swelling, as characterized by the spatial extension of the
chain, scales with the monomer number defining a Flory exponent $\nu$ which is
$\nu =1/2, 0, 1$ in the three different situations. As a result, we find that
activity does not change the Flory exponent but affects the prefactor of the
scaling law. This can be quantitatively understood by mapping the system onto
an equilibrium chain with a higher effective temperature such that the chain
swells under an increase of the self-propulsion strength. We then use computer
simulations to study the effect of self-avoidance on active polymer swelling.
In the three different situations, the Flory exponent is now $\nu = 3/4, 1/4,
1$ and again unchanged under self-propulsion. However, the chain extension
behaves non-monotonic in the self-propulsion strength.
