Missing negative sign in my textbook's answer?

[mymodded]

Homework Statement

A coil with N turns and area A, carrying a constant current, flips in an external field $\vec{B}_{ext}$ , so that its dipole moment switches from opposition to the field to alignment with the field. During this process, induction produces a potential difference that tends to reduce the current in the coil. Calculate the work done by the coil's power supply to maintain the constant current.

Relevant Equations

$W = \int_{\theta_{i}}^{\theta_{f}} \tau (\theta) d\theta$
or
$U(\theta) = -NiABcos(\theta)$

the question is fairly easy to solve, integrating $NiAB sin(\theta)$ from $\pi$ to 0 or just do $-NiAB(cos(0) - cos(\pi))$ which gives you -2NiAB, but my textbook did not include the negative sign, is it mistaken?

 

[anuttarasammyak]

Your minus answer is the work external force did. Battery cell did minus counter work, so it is plus.