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Question Number 126997 by bramlexs22 last updated on 26/Dec/20

  ∫_0 ^1  arcsin (((sin x)/( (√2)))) dx =?

10arcsin(sinx2)dx=?

Answered by Evimene last updated on 26/Dec/20

solution  let (√2)=α  f(α)=∫_0 ^1 arcsin(((sinx)/α))dx⇔differentiating α  f′(α)=∫_0 ^1 (α^2 /(α^2 −sin^2 x))dx⇔multiply by ((sec^2 x)/(sec^2 x))  f^′ (α)=∫_0 ^1 ((α^2 sec^2 x)/(α^2 sec^2 x−α^2 tan^2 x))dx⇔recall sec^2 x+tan^2 x=1  f′(α)=∫_0 ^1 sec^2 xdx;⇔[tanx]_0 ^1   f^1 (α)=(π/4)  f(α)=(π/4)x+c⇔f(0)=0;so c=0  f(α)=(π/4)  cadet praise

solutionlet2=αf(α)=01arcsin(sinxα)dxdifferentiatingαf(α)=01α2α2sin2xdxmultiplybysec2xsec2xf(α)=01α2sec2xα2sec2xα2tan2xdxrecallsec2x+tan2x=1f(α)=01sec2xdx;[tanx]01f1(α)=π4f(α)=π4x+cf(0)=0;soc=0f(α)=π4cadetpraise

Commented by bramlexs22 last updated on 26/Dec/20

Feynmann method?

Feynmannmethod?

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