"were actively engaged" is correct and can be used in written English.
You can use it to indicate that someone was actively involved in an activity or task. For example, "The students were actively engaged in the project, working together to find solutions."
Several massage therapists suggested that they were actively engaged in activities not only to market their services but also more broadly promote the massage therapy profession.
A team of neuroscientists led by Eleanor Maguire at University College London wanted to monitor brain activity while people were actively engaged in navigation.
They were actively engaged in various activities to improve their surroundings.
The present study revealed that Indian repositories were actively engaged in data curation activities, depositing a wide variety of items in their respective IRs.
From 1968-1972, inmates athehe Penitentiary of New Mexico were actively engaged in opportunities stemming from civic engagement within the prison environment (Colvin 2007).
This was calculated for both the patient and the caretaker who were actively engaged in an income-generating activity prior to the illness.
Regarding the effect of gamified interactive display technology as a means of consolidating knowledge and improving engagement, the field study demonstrated that students enjoyed the game and were actively engaged; they liked playing in groups or competing with each other.
The participants were key personnel, representing the organizations, who were actively engaged in contract manufacturing services.
Both Greeks and Phoenicians were actively engaged in trade with the Italian natives.
Its research shows that 4.5m women were actively engaged with the Premier League during the 2013-14 season.
When the subjects were actively engaged with Facebook, their physiological response measured a significant uptick in happiness.
