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Question Number 194649 by SANOGO last updated on 12/Jul/23

calcul   ∫_0 ^(Π/2) (√(4sin^2 t+cos^2 t ))dt

calcul0Π24sin2t+cos2tdt

Commented by Frix last updated on 12/Jul/23

You changed the question... but  4sin^2  t +cos^2  t =1+3sin^2  t  so the answer is the same.

Youchangedthequestion...but4sin2t+cos2t=1+3sin2tsotheansweristhesame.

Commented by SANOGO last updated on 12/Jul/23

ok thank you

okthankyou

Commented by Frix last updated on 12/Jul/23

∫(√(1+3sin^2  t)) dt=E (t∣−3) +C  [complete elliptic integral of the 2^(nd)  kind]  ∫_0 ^(π/2) (√(1+3sin^2  t)) dt≈2.42211206

1+3sin2tdt=E(t3)+C[completeellipticintegralofthe2ndkind]π201+3sin2tdt2.42211206

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