Asked by Jay
Evaluate
π
∫ tan² x/3 dx
0
π
∫ tan² x/3 dx
0
Answers
Answered by
Reiny
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
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
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