Question

Evaluate

π
∫ tan² x/3 dx
0

Answer 1

recall that tan^2 A +1 = sec^2 A

and d(tanA)/dA = sec^2 A

so ∫ tan² x/3 dx
= ∫ sec^2 (x/3) - 1 dx form 0 to π
= [3 tan (x/3) - x] from 0 to π
= 3tan π/3 - π -(3tan 0 - 0)
= 3 √3 - π